Raport stiintific final de evaluare a proiectului PN-III-P4-ID-PCE-2016-0011

,,Analiza si controlul ecuatiei stochastice Schrödinger si a unor modele de

difuzie neliniara” in perioada 12.07.2017-30.12.2019

Obiective: Studiul problemei de control optimal atasata ecuatiei stochastice Schrodinger (existenta si

principiul de maxim) si construirea unui control feedback pentru aceasta problema ca si pentru

problema urmaririi orbitei pe liniile prezentate anterior. O teorie de existenta riguroasa pentru o

problema stochastica parabolica si tehnici de restaurare a imaginilor bazate pe aceasta ecuatie cu

neliniaritate nemonotona a similara celei din modelul Perona-Malik. Analiza si aproximarea unor

modele matematice in biologie.

2017

In anul 2017, in cadrul proiectului PN-III-P4-ID-PCE-2016-0011 s-au realizat urmatoarele:

- 1 lucrare publicata in revista internationala ISI.

1. Viorel Barbu, Michael Röckner, Deng Zhang, Stochastic nonlinear Schrödinger

equations: No blow-up in the non-conservative case, J. Differential Equations, vol.

263, issue 11 (2017), 7919--7940. FI=1.938, SRI=2.408, SNIP=1.710.

Abstract. This paper is devoted to the study of noise effects on blow-up solutions to stochastic

nonlinear Schrödinger equations. It is a continuation of our recent work [2], where the (local) well-

posedness is established in H1, also in the non-conservative critical case. Here we prove that in the non-

conservative focusing mass-(super)critical case, by adding a large multiplicative Gaussian noise, with

high probability one can prevent the blow-up on any given bounded time interval [0,T], 0<T<∞.

Moreover, in the case of spatially independent noise, the explosion even can be prevented with high

probability on the whole time interval [0,∞). The noise effects obtained here are completely different

from those in the conservative case studied in [5].

- 2 lucrari in curs de finalizare

a. Gabriela Marinoschi, Analiza si aproximarea unor modele matematice in biologie

bazate pe ecuatii parabolice

b. Tudor Barbu, O lucrare privind studiul problemei de restaurare a imaginilor folosind

argumente stochastice.

- 5 conferinte:

1. Viorel Barbu, The dynamic programming equation for the Heston stochastic optimal

control problem, Worshop international "Current Trends in Applied Mathematics",

Iasi, 27-28 octombrie 2017.

2. Gabriela Marinoschi, A singular nonconvex optimal control problem with application

to image denoising, Worshop international "Current Trends in Applied Mathematics",

Iasi, 27-28 octombrie 2017.

3. Ionut Munteanu, Boundary stabilization to trajectories for parabolic-like equations,

Worshop international "Current Trends in Applied Mathematics", Iasi, 27-28

octombrie 2017.

4. Elena-Alexandra Melnig, Feedback stabilization with simultaneous control for a

coupled parabolic system, Worshop international "Current Trends in Applied

Mathematics", Iasi, 27-28 octombrie 2017.

5. Alexander Zaslavski, Turnpike properties in the calculus of variations and optimal

control (colaborator), Worshop international "Current Trends in Applied

Mathematics", Iasi, 27-28 octombrie 2017.

- 1 workshop organizat: a. Worshopul international "Current Trends in Applied Mathematics", Iasi, 27-28 octombrie 2017.

- alte activitati: A fost realizata pagina web a proiectului: http://acsn.acadiasi.ro/

2018

In anul 2018 in cadrul proiectului PN-III-P4-ID-PCE-2016-0011 s-au realizat urmatoarele:

- 10 lucrari publicate in reviste internationale ISI.

1. Viorel Barbu, Chiara Benazzoli, Luca Di Persio, Mild solutions to the dynamic program-

ming equation for stochastic optimal control problems, Automatica 93 (2018), 520–526.

FI=6.355, SRI=4.827, SNIP=3.107.

Abstract. We show via the nonlinear semigroup theory in L1(R) that the 1-D dynamic programming equation

associated with a stochastic optimal control problem with multiplicative noise has a unique mild solution in

a sense to be made precise.

2. Viorel Barbu, Michael Röckner, Deng Zhang, Optimal bilinear control of nonlinear stochastic

Schrödinger equations driven by linear multiplicative noise, The Annals of Probability, 2018, Vol.

46, No. 4, 1957–1999 https://doi.org/10.1214/17-AOP1217.

Abstract. We analyze the bilinear optimal control problem of quantum mechanical systems with final observation

governed by a stochastic nonlinear Schrödinger equation perturbed by a linear multiplicative Wiener process. The

existence of an open-loop optimal control and first-order Lagrange optimality conditions are derived, via Skorohod’s

representation theorem, Ekeland’s variational principle and the existence for the linearized dual backward stochastic

equation. Moreover, our approach in particular applies to the deterministic case.

3. Viorel Barbu, Michael Röckner, Variational solutions to nonlinear stochastic differential

equations in Hilbert spaces, Stochastics and Partial Differential Equations. Analysis and

Computations, 6 (3) (2018), 500-524. Abstract. One introduces a new variational concept of solution for the stochastic differential equation

dX + A(t)X dt + λX dt = X dW, t ∈ (0, T ); X(0) = x in a real Hilbert space where A(t) = ∂ϕ(t), t ∈ (0, T ),

is a maximal monotone subpotential operator in H while W is a Wiener process in H on a probability space

{Ω,F, P}. In this new context, the solution X = X(t, x) exists for each x ∈ H, is unique, and depends conti-

nuously on x. This functional scheme applies to a general class of stochastic PDE so far not covered by the

classical variational existence theory (Krylov and Rozovskii in J Sov Math 16:1233–1277, 1981; Liu and

Röckner in Stochastic partial differential equations: an introduction, Springer, Berlin, 2015; Pardoux in

Equations aux dérivées partielles stochastiques nonlinéaires monotones, Thèse, Orsay, 1972) and, in particu-

lar, to stochastic variational inequalities and parabolic stochastic equations with general monotone nonlinea-

rities with low or superfast growth to +∞.

4. Viorel Barbu, Michael Röckner, Nonlinear Fokker–Planck equations driven by Gaussian

linear multiplicative noise, J. Differential Equations, 265 (2018) 4993–5030. FI=1.938,

SNIP=1.710, SRI=2.408.

Abatract. Existence of a strong solution in H−1(ℝd) is proved for the stochastic nonlinear Fokker–Planck equation res-

pectively, for a corresponding random differential equation. Here d≥1, W is a Wiener process in H−1(ℝd), D∈C1(ℝd, ℝd)

and β is a continuous monotonically increasing function satisfying some appropriate sublinear growth conditions which

are compatible with the physical models arising in statis-tical mechanics. The solution exists for x∈L1∩L∞ and preserves

positivity. If β is locally Lipschitz, the solution is unique, pathwise Lipschitz continuous with respect to initial data in

H−1(ℝd). Stochastic Fokker–Planck equations with nonlinear drift of the form dX−div(a(X))dt−β(X)dt=XdW are also

considered for Lipschitzian continuous functions a:R → ℝd.

5. P. Colli, G. Gilardi, Gabriela Marinoschi, E. Rocca, Sliding mode control for phase field

system related to tumor growth, Appl. Math.Optimiz., 79 (3) (June 2019), 647–670. FI= 1.895,

SRI= 1.560 , ISSN: 0095-4616. (Print), 1432-0606 (Online) [raportat in 2018 ca publicat online]

Abstract. In the present contribution we study the sliding mode control (SMC) problem for a diffuse interface

tumor growth model coupling a viscous Cahn--Hilliard type equation for the phase variable with a reaction-

diffusion equation for the nutrient. First, we prove the well-posedness and some regularity results for the

state system modified by the state-feedback control law. Then, we show that the chosen SMC law forces the

system to reach within finite time the sliding manifold (that we chose in order that the tumor phase remains

constant in time). The feedback control law is added in the Cahn--Hilliard type equation and leads the phase

onto a prescribed target φ* in finite time.

6. T. Barbu, Second-order anisotropic diffusion-based framework for structural inpainting,

Proceedings of the Romanian Academy, Series A: Mathematics, Physics, Technical

Sciences, Information Science, Volume 19, Number 2, pp. 329-336, April - June 2018.

Abstract. A novel structure-based image interpolation technique is proposed in this paper. It is based on a

nonlinear anisotropic diffusion model that is properly constructed for the reconstruction process. A rigorous

mathematical investigation of this partial differential equation (PDE)-based scheme is then performed, its

well-posedness being treated. An explicit finite difference-based numerical approximation scheme that is

consistent to the second-order PDE model and converges to its weak solution is developed next. The

successful inpainting experiments and method comparison prove the effectiveness of the considered

diffusion-based approach.

7. T. Barbu, Additive noise removal using a nonlinear hyperbolic PDE-based model,

Proceedings of the International Conference on Development and Application Systems,

DAS 2018, Suceava, Romania, pp. 1-5, 24-26 May 2018, IEEE.

Abstract. A novel second-order partial differential equation (PDE) - based image restoration technique is

proposed here. The considered denoising method is based on a nonlinear hyperbolic differential model

combined to a two-dimension filter kernel. The considered PDE model is well-posed and it is solved

numerically by constructing an explicit iterative finite difference-based numerical approximation algorithm

that is consistent to the combined PDE model and converges fast to its weak solution. Our successful

restoration experiments and method comparison are also discussed.

8. T. Barbu, Compound Hyperbolic PDE-based Additive Gaussian Noise Removal Solution

combining Second- and Fourth-order Diffusions, Proceedings of 10th International

Conference on Electronics, Computers and Artificial Intelligence, ECAI 2009, Iași,

Romania, June 28–30, 2018, IEEE.

Abstract. A hybrid nonlinear PDE-based denoising framework is proposed in this paper. The considered

image restoration technique is based on a well-posed hyperbolic differential model that combines second-

and fourth-order diffusions. A consistent finite difference-based numerical approximation algorithms is then

constructed for solving this hyperbolic diffusion-based model. Our successful restoration experiments that

illustrate the effectiveness of the proposed method are also discussed.

9. Ionut Munteanu: Boundary stabilization of the stochastic heat equation by proportional

feedbacks, Automatica 87 (2018),152-158. FI=6.355, SRI=4.827, SNIP=3.107.

Abstract: In this work we design an explicit random deterministic, finite-dimensional stabilizing boundary

feedback to the null solution for the heat equation with noise perturbation. The simple form of the feedback

allows us to write the solution of the corresponding closed-loop equation in a mild formulation via a kernel

and use some techniques from the existing literature in order to show the stability of it. As far as we know,

the present work is the first result on boundary feedback stabilization for stochastic parabolic-type equations,

with the stability guaranteed independent of how large the level of the noise is.

10. Ionut Munteanu, Boundary stabilisation to non-stationary solutions for deterministic

and stochastic parabolic-type equations, International Journal of Control, https://doi.org/

10.1080/00207179.2017.1407878. FI= 2.101, SRI=1.249.

Abstract. In this work, we design explicit, finite-dimensional boundary feedback laws for stabilization to

trajectories for parabolic-type equations. The simple form of the feedback allows to write the solution of the

corresponding closed-loop equation in a mild formulation via a kernel; then, taking advantage of this, the

stability is shown. As an application, null stabilization for stochastic parabolic-type equations is deduced as

well. As far as we know, the present work is the first result on boundary feedback stabilization to trajectories

and for stochastic parabolic-type equations, with stability guaranteed independent of how large the level of

the noise is.

- 5 conferinte:

1. G. Marinoschi, An Optimal Control Approach to the Optical Flow Problem, Conference

"Challenges in Optimal Control of Nonlinear PDE-Systems", Oberwolfach, Germany,

9-14 April 2018.

2. Tudor Barbu, A Nonlinear Second-order Partial Differential Equation-based Algorithm for

Additive Noise Reduction, International Conference on Mathematics and Computer Science,

MACOS 2018, Brasov, Romania, June 14-16, 2018.

3. Tudor Barbu, Overview of Nonlinear Partial Differential Equation-based Structural Inpainting

Techniques, Plenary Speech at 26th International Conference on Applied and Industrial

Mathematics, CAIM 2018, Chișinău, Moldova, September 20-23, 2018.

4. Tudor Barbu, Hyperbolic second-order partial differential equation-based model for structural

interpolation, The XII-th International Conference of Differential Geometry and Dynamical

Systems (DGDS-2018), Mangalia, Romania, 30 August - 2 September 2018.

5. Elena-Alexandra Melnig, Lq estimates for inverse source parabolic problems, Geometry and

PDE’s Workshop, Timisoara, 11-14 octombrie 2018.

- 1 workshop organizat: Workshopul international "Current Trends in Applied Mathematics",

Iasi, 10-11 Septembrie 2018, organizat de Institutul de Matematica Octav Mayer in cola-

borare cu Institutul de Statistici Matematice si Matematici Aplicate Bucuresti.

- s-a actualizat pagina web a proiectului:

http://acsn.acadiasi.org/wp-content/uploads/2018/12/

2019

In anul 2019, in cadrul proiectului PN-III-P4-ID-PCE-2016-0011 s-au realizat urmatoarele:

5 lucrari publicate in reviste internationale ISI.

1. Viorel Barbu, L. Tubaro, Exact controllability of stochastic differential equations with

multiplicative noise, Systems & Control Letters, 122 (2018), 19–23. FI=2.624, SRI=2.217,

SNIP=1.485. ISSN= 0167-6911. (neraportat in 2018)

Abstract. One proves that the n-D stochastic controlled equation dX(t) + A(t)X(t) dt = σ(X(t))dW(t) +

B(t)u(t)dt, where σ ∈ Lip(Rn,L(Rd, Rn)), A(t) ∈ L(Rn) and B(t) ∈ L(Rn, Rn) is invertible, is exactly controllable

with high probability in each y ∈ Rn such that σ(y) = 0 on each finite interval (0,T). An application to

approximate controllability of the stochastic heat equation is given. The case where B∈L(Rm, Rn), 1 ≤ m < n

and the pair (A, B) satisfies the Kalman rank condition is also studied.

2. Viorel Barbu, The dynamic programing equation for a stochastic volatility optimal control

problem, Automatica, 107 (2019), 119-124. FI=6.355, SRI=4.827, SNIP=3.107.

Abstract. In this note, one constructs a distributional solution to the d-dimensional dynamic programming

equation, d ≥ 3, for an optimal control problem governed by a stochastic volatility model. The approach is

based on nonlinear semigroup theory in the space L1(Rd).

3. G. Marinoschi, Rescaling approach for a stochastic population dynamics equation

perturbed by a linear multiplicative Gaussian noise, Appl. Math. Optimiz. DOI:

10.1007/s00245-018-9507-8. FI=1.301, SRI=1.788 (online published). ISSN: 0095-4616

(Print) 1432-0606 (Online)

Abstract. We are concerned with a nonlinear nonautonomous model represented by an equation describing

the dynamics of an age-structured population diffusing in a space habitat O, governed by local Lipschitz vital

factors and by a stochastic behavior of the demographic rates possibly representing emigration, immigration

and fortuitous mortality. The model is completed by a random initial condition, a flux type boundary

conditions on ∂O with a random jump in the population density and a nonlocal nonlinear boundary condition

given at age zero. The stochastic influence is expressed by a linear multiplicative Gaussian noise perturbation

in the equation. The main result proves that the stochastic model is well-posed, the solution being in the class

of path-wise continuous functions and satisfying some particular regularities with respect to the age and

space. The approach is based on a rescaling transformation of the stochastic equation into a random

deterministic time dependent hyperbolic-parabolic equation with local Lipschitz nonlinearities. The existence

and uniqueness of a strong solution to the random deterministic equation is proved by combined semigroup,

variational and approximation techniques. The information given by these results is transported back via the

rescaling transformation towards the stochastic equation and enables the proof of its well-posedness.

4. Pierluigi Colli, Gianni Gilardi, Ionuț Munteanu, Stabilization of a linearized Cahn–

Hilliard system for phase separation by proportional boundary feedbacks, Internat. J.

Control, doi: 10.1080/ 00207179.2019.1597280. FI=2.101, SRI= 1.249 . Print ISSN: 0020-

7179. Online ISSN: 1366-5820.

Abstract. This work represents a first contribution on the problem of boundary stabilization for the phase

field system of Cahn-Hilliard type, which models the phase separation in a binary mixture. The feedback

controller we design here is with actuation only on the temperature flow of the system, on one part of the

boundary only. Moreover, it is of proportional type, given in an explicit form, expressed only in terms of the

eigenfunctions of the Laplace operator, being easy to manipulate from the computational point of view.

Furthermore, it ensures that the closed loop nonlinear system exponentially reaches the prescribed stationary

solution provided that the initial datum is close enough to it.

5. Catalin-George Lefter, Elena-Alexandra Melnig, Feedback stabilization with one

simultaneous control for systems of parabolic equations, Mathematical Control and

Related Fields, September 8 (3&4) (2018), 777-787. doi: 10.3934/mcrf.2018034.

FI=1.292, SRI=1.022, ISSN=2156-8472. (nu a fost raportat in 2018).

Abstract. In this work controlled systems of semilinear parabolic equations are considered. Only one control

is acting in both equations and it is distributed in a subdomain. Local feedback stabilization is studied. The

approach is based on approximate controllability for the linearized system and the use of an appropriate norm

obtained from a Lyapunov equation. Applications to reaction-diffusion systems are discussed.

1 capitol de carte

1. Tudor Barbu, A Survey on Nonlinear Second-order Diffusion-based Techniques for

Additive Denoising, Soft Computing Applications. Advances in Intelligent Systems and

Computing, Balas V., Jain L., Balas M. (eds), Springer, 2019, ISSN 2194-5357, to appear.

Abstract. An overview of additive noise removal algorithms using secondorder nonlinear partial differential

equations (PDEs) is provided in this paper. The state of the art anisotropic diffusion models for image

restoration are described first. Then, the second-order PDE-based denoising approaches using variational

schemes are addressed. Our most important contributions in these image processing fields are also mentioned

in this work.

9 lucrari elaborate/trimise/acceptate la publicare

1. G. Marinoschi, Minimal time sliding mode control for evolution equations in Hilbert

spaces, ESAIM-COCV, doi: 10.1051/cocv/2019065. ISI. FI=1.295, SRI=2.086, acceptata.

Abstract. This work is concerned with the time optimal control problem for evolution equations in Hilbert

spaces. The attention is focused on the maximum principle for the time optimal controllers having the

dimension smaller that of the state system, in particular for minimal time sliding mode controllers, which is

one of the novelties of this paper. We provide the characterization of the controllers by the optimality

conditions determined for some general cases. The proofs rely on a set of hypotheses meant to cover a large

class of applications. Examples of control problems governed by parabolic equations with potential and drift

terms, porous media equation or reaction-diffusion systems with linear and nonlinear perturbations, descri-

bing real world processes, are presented at the end.

2. Pierluigi Colli, Hector Gomez, Guillermo Lorenzo, Gabriela Marinoschi, Alessandro Reali,

Elisabetta Rocca, Mathematical analysis and simulation study of a phase-field model of

prostate cancer growth with chemotherapy and antiangiogenic therapy effects,

arXiv:1907.11618v1 [math.AP] 26 Jul 2019.

Abstract. Chemotherapy is a common treatment for advanced prostate cancer. The standard approach relies

on cytotoxic drugs, which aim at inhibiting proliferation and promoting cell death. Advanced prostatic tumors

are known to rely on angiogenesis, i.e., the growth of local microvasculature via chemical signaling produced

by the tumor. Thus, several clinical studies have been investigating antiangiogenic therapy for advanced

prostate cancer, either as monotherapy or in combination with standard cytotoxic protocols. However, the

complex genetic alterations that originate and sustain prostate cancer growth complicate the selection of the

best chemotherapeutic approach for each patient's tumor. Here, we present a mathematical model of prostate

cancer growth and chemotherapy that may enable physicians to test and design personalized

chemotherapeutic protocols in silico. We use the phase-field method to describe tumor growth, which we

assume to be driven by a generic nutrient following reaction-diffusion dynamics. Tumor proliferation and

apoptosis (i.e., programmed cell death) can be parameterized with experimentally-determined values.

Cytotoxic chemotherapy is included as a term downregulating tumor net proliferation, while antiangiogenic

therapy is modeled as a reduction in intratumoral nutrient supply. An additional equation couples the tumor

phase field with the production of prostate-specific antigen, which is a prostate cancer biomarker that is

extensively used in the clinical management of the disease. We prove the well-posedness of our model and

we run a series of representative simulations leveraging an isogeometric method to explore untreated tumor

growth as well as the effects of cytotoxic chemotherapy and antiangiogenic therapy, both alone and

combined. Our simulations show that our model captures the growth morphologies of prostate cancer as well

as common outcomes of cytotoxic and antiangiogenic mono and combined therapy. Additionally, our model

also reproduces the usual temporal trends in tumor volume and prostate-specific antigen evolution observed

in experimental and clinical studies.

3. T. Barbu, Detail-preserving Fourth-order Nonlinear PDE-based Image Restoration

Framework, Journal of Image and Graphics, to appear in 2019.

Abstract. A novel fourth-order partial differential equation (PDE) – based image restoration technique is

proposed in this work. It is based on a well-posed fourth-order nonlinear diffusion-based model combined to

a two-dimension filter kernel. An iterative finite difference-based numerical approximation algorithm is then

constructed for solving the PDE model. The proposed approach removes successfully the additive noise,

overcome unintended effects like the staircasing and preserves successfully the edges and other image details.

4. Tudor Barbu, Second-Order Anisotropic Diffusion-Based Technique for Poisson

Noise Removal, IFAC Papers-on-line (Proceedings of the Joint IFAC Conference 7th

SSSC 2019 and 15th TDS 2019), 9-11 September 2019, Sinaia, Romania, pp. 174-178,

to appear.

Abstract: A partial differential equation (PDE) – based technique for filtering the Poisson noise from digital images is

proposed in this work. It is based on a nonlinear second-order anisotropic diffusionbased model that is adapted for the

Poisson distribution. The considered PDE model is well-posed and its unique and weak solution is computed using a

finite difference-based numerical approximation scheme that is consistent to the proposed model. The proposed approach

provides an effective feature-preserving Poisson denoising. Some results of our filtering simulations are also described

in this paper.

5. Catalin-George Lefter, Elena-Alexandra Melnig, On the parabolic regularity, Sobo-

lev embeddings and global Carleman estimates in Lq(Lp) spaces, Pure and Applied

Functional Analysis, acceptata. ISSN 2189-3756.

Abstract. In this paper we discuss some aspects related to regularity in parabolic problems with corollaries

regarding anisotropic Sobolev embeddings. We use these results in the context of bootstrap arguments applied

to global Carleman estimates for nonhomogeneous parabolic equations in Lqt(Lp

x) spaces, estimates which

are fundamental in associated control and inverse problems. The arguments we use are characterizations of

regularity in terms of domains of fractional powers of elliptic operators and then characterization of these

domains as interpolation spaces and relations to Bessel potential and Sobolev-Slobodeckii spaces.

6. Viorel Barbu, Michael Röckner, The evolution to equilibrium of solutions to

nonlinear Fokker-Planck equation.

Abstract. One proves the H-theorem for mild solutions to a nondegenerate, nonlinear Fokker-Planck

equation (1) ut -ΔΔβ(u) + div(D(x)b(u)u) = 0, t > 0, x → Rd, and under appropriate hypotheses on β, D and b the convergence in L1

loc(Rd), L1(Rd), respectively, for some

tn →∞ of the solution u(tn) to an equilibrium state of the equation for a large set of nonnegative initial data in

L1. Furthermore, the solution to the McKean-Vlasov stochastic differential equation corresponding to (1),

which is a nonlinear distorted Brownian motion, is shown to have this equilibrium state as its unique invariant

measure.

7. Viorel Barbu, Michael Röckner, From nonlinear Fokker-Planck equations to

solutions of distribution dependent SDE.

Abstract. We construct weak solutions to the McKean-Vlasov SDE

dX(t) = b(X(t),(dLX(t)/dx)(X(t)))dt+σ(X(t),(dLX(t)/dx)(X(t)))dW(t)

on Rd for possibly degenerate diffusion matrices σ with X(0) having a given law, which has a density with

respect to Lebesgue measure, dx. Here LX(t) denotes the law of X(t). Our approach is to first solve the

corresponding nonlinear Fokker-Planck equations and then use the well known superposition principle to

obtain weak solutions of the above SDE.

8. Elena-Alexandra Melnig, Stability in Lq-norm for inverse source parabolic problems,

submitted to Journal of Inverse and Ill Posed Problems. (ISI)

Abstract.We consider systems of parabolic equations coupled in zero and first order terms. We establish

Lipschitz estimates in Lq-norms, 2 < q < ∞ for the source in terms of the solution in a subdomain. The main

tool is a family of appropriate Carleman estimates with general weights, in Lebesgue spaces, for

nonhomogeneous parabolic systems.

9. Elena-Alexandra Melnig, Stability in inverse source problems for nonlinear reaction-

diffusion systems, submitted to Nonlinear Differential Equations and Applications.

(ISI)

Abstract. We consider coupled parabolic systems with homogeneous boundary conditions. We establish a

family of Lq-Carleman inequalities, q\in[2,∞) and use them to obtain stability estimates in Lq and L∞ norms

for the sources in terms of the solution in a subdomain. We apply these estimates to reaction-diffusion

systems.

6 Conferinte

1. Viorel Barbu, The H-theorem for the nonlinear Fokker-Planck equations, conferința

“New Perspectives in Nonlinear PDE”, The Center for Mathematical Sciences (CMS),

Technion, Israel, 31.05-07.06.2019.

2. Viorel Barbu, Stochastic Differential Equations (16 conferințe de o oră în vederea dise-

minării rezultatelor științifice din tematica proiectului PN-III-P4-ID-PCE-2016-0011),

6 aprilie-7 mai 2019, Universitatea din Trento, Italia (Departamentul de matematică).

3. Viorel Barbu, Asymptotic fedback controllability of Fokker-Planck equations, „Special

Semester on Optimization 2019, Workshop 5 – Feedback control” at RICAM, Linz, Austria”,

28-30 nov. 2019, Linz, Austria.

4. Gabriela Marinoschi, Feedback stabilization of a phase-field system with viscosity effects, „Special Semester on Optimization 2019, Workshop 5 – Feedback control” at RICAM, Linz,

Austria”, 28-30 nov. 2019, Linz, Austria.

5. T. Barbu, Structural Inpainting Techniques using Equations of Engineering Physics, prezentata la

conferinta 19th International Balkan Workshop on Applied Physics and Materials Science, IBWAP

2019, July 16-19, 2019, Constanta, Romania.

6. Tudor Barbu, Fourth-order Nonlinear PDE-based Image Restoration Framework,

prezentata la The 8th International Conference on Pure and Applied Mathematics - ICPAM

2019, Bruxelles, Belgia, 22-25 iulie 2019.

3 Stagii de cercetare

1. Viorel Barbu, Stagiu de cercetare cu grupul “Taming uncertainty and profiting from

randomness and low regularity in analysis, stochastic and their applications” din cadrul

Universitatii din Bielefeld, în perioada 05 august – 05 septembrie 2019.

2. Gabriela Marinoschi, stagiu de cercetare la Instituto di Analisi dei Sistemi ed Informatica

“Antonio Ruberti” (IASI), Roma, Italia, in perioada 19-16 septembrie 2019.

3. Ionuț Munteanu, Stagiu de cercetare împreună cu P. Colli, 14-20 Octombrie 2019,

Universitatea din Pavia, Italia.

- s-a actualizat pagina web a proiectului: https://acsn.acadiasi.org/

DIRECTOR DE PROIECT,

Acad. Viorel Barbu