Romanian version here.

Grant PN-II-ID-PCE-2011-3-0075, Contract 146/05/10/2011 financed by CNCS-UEFISCDI, ANCS

Host institution IMAR.

Title: Analysis, control and numerical approximation for partial differential equations.

Abstract. This project is devoted to the analytic and numerical study of Partial Differential Equations. More precisely we treat problems related with their well-posedness, control, optimization, inverse problems and numerical approximation.

We distinguish the following areas and work subjects

A. Analysis and control of PDE (L. Ignat, C. Cazacu, A. Marica, A. Grecu),

B. Elliptic PDEs, variational inequalities, equations on fractals (M.Mihailescu, N. Costea, D. Stancu-Dumitru),

C. Numerical Methods for the control and simulation of PDEs (A. Marica, L. Ignat, C. Cazacu).

TEAM

1. Liviu Ignat

2. Mihai Mihailescu

3. Aurora Marica

4. Nicusor Costea

5. Cristi Cazacu

6. Denisa Stancu

7. Gabriela Olaru

8. Andreea Grecu

9. Octavian Mustafa (former member of the grant)

Report 2011, PDF

Report 2012, PDF,

Report 2011-2013 cumulative for the first evaluation, PDF

Report 2014, PDF

Report 2015, PDF

Report 2016, PDF

Budget, PDF

Report 2011-20136 cumulative, PDF

Expected results:

We want to obtain new results regarding well-posedness and numerical approximation of some equations that arise from some physical models.

Brief description of the expected objectives

A. Analysis and control of PDE

a) Dispersion under general coupling conditions on networks; b) Magnetic Scrodinger equations; c) Carleman inequalities and inverse problems on networks; d) Control of PDEs with singular coefficients and potentials located on the boundary; e) Evolution equations.

B. Elliptic PDEs, variational inequalities, equations on fractals

a) Equations involving variable exponent growth conditions; b) Equations involving nonlinear and nonhomogeneous operators analyzed in the framework of Orlicz-Sobolev spaces; c) Differential inclusions for multivalued functionals involving second-order quasilinear elliptic differential operators of the Leray-Lions type; d) Differential inclusions for multivalued functionals involving nonhomogeneous and nonlinear differential operators; e) Equations involving the Laplacian on the Sierpinski gasket.

C. Numerical Methods for the control and simulation of PDEs.

a) Propagation of discrete waves and their dispersive properties in non-uniform meshes and heterogeneous media, appropriate definition of the principal symbol; representation formulas for the numerical solutions following the pseudo- differential calculus; constructing bi-characteristic rays; describing unexpected dispersion phenomena due to the irregularity of the mesh like the torsion of the rays; b) Designing efficient bi-grid algorithm on non-uniform meshes; c) Gaussian beam-like solutions; d) Numerical methods for problems with singular coefficients by means of a posteriori estimates;

The results obtained in this project are collected in the following articles.

Papers

1. Mihai Mihăilescu, Dušan Repovš, On a PDE involving the Ap(·)-Laplace operator, Nonlinear Analysis 75 (2012) 975–981, PDF

2. Cristian Cazacu, Hardy inequality and Pohozaev identity for operators withboundary singularities: some applications,

C. R. Acad. Sci. Paris, Ser. I 349 (2011) 1167–1172, PDF

3. L. Ignat, A. Pazoto, L. Rosier, INVERSE PROBLEM FOR THE HEAT EQUATION AND THESCHRODINGER EQUATION ON A TREE,

Inverse Problems 28 (2012), no. 1, 015011, 30 pp, PDF

4. Denisa Stancu Dumitru, TWO NONTRIVIAL WEAK SOLUTIONS FOR THE DIRICHLET PROBLEM ON THE SIERPINSKI GASKET,

Bull. Aust. Math. Soc., 85 (2012), 395-414, PDF.

5. L. Ignat, E. Zuazua, Convergence rates for dispersive approximation schemes to nonlinear Schr\"odinger equations, J. Math. Pures Appl. (9) 98 (2012), no. 5, 479–517, PDF

6. Mihai Mihăilescu, Denisa Stancu Dumitru, Anisotropic quasilinear elliptic equations with variable exponent, J. Korean Math. Soc. 49 (2012), No. 6, pp. 1123–1138, PDF

7. Cristian Cazacu, Schrödinger operators with boundary singularities: Hardy inequality, Pohozaev identity and controllability results, Journal of Functional Analysis, Volume 263, Issue 12, 15 December 2012, Pages 3741–3783, PDF

8.L. Ignat, E. Zuazua, Asymptotic expansions for anisotropic heat kernels, J. Evol. Equ. 13 (2013), 1–20, PDF

9. Denisa Stancu, Variational treatment of nonlinear equations on the Sierpinski gasket, Complex Var. Elliptic Equ. 59 (2014), no. 2, 172–189, PDF

10. Dumitru Baleanu, Octavian Mustafa, Donal O’Regan, On a fractional differential equation with infinitely many solutions, Advances in Difference Equations 2012, 2012:145, PDF

11. Marica A., Zuazua E., On the quadratic finite element approximation of 1-d waves: propagation, observation and control, SIAM J. Numer. Anal., 50(5), 2012, 2744–2777, PDF

12. Marica A., Zuazua E.,Symmetric discontinuous Galerkin methods for 1-D waves. Fourier analysis, propagation, observability and applications. With a foreword by Roland Glowinski. Springer Briefs in Mathematics.Springer, New York, 2014. xvi+104 pp. ISBN: 978-1-4614-5810-4; 978-1-4614-5811-1

13. Marica A., Zuazua E., On the quadratic finite element approximation of 1-d waves: propagation, observation, control

and numerical implementation, ``CFL-80: A Celebration of 80 Years of the Discovery of CFL Condition", C. Kubrusly and C. A. Moura, eds., Springer Proceedings in Mathematics, Springer Verlag, PDF

14. C. Cazacu and E. Zuazua, Improved multipolar Hardy inequalities, "Studies in Phase Space Analysis of PDE's", Birkhauser series "Progress in Nonlinear Differential Equations and Their Applications", ISBN 978-1-4614-6347-4, pp 35-52, PDF

15. V. Banica, L. I. Ignat, Dispersion for the Schr"odinger equation on the line with multiple Dirac delta potentials and on delta trees, Anal. PDE 7 (2014), no. 4, 903–927, PDF

16. Liviu I. Ignat, Tatiana I. Ignat, Denisa Stancu-Dumitru, A COMPACTNESS TOOL FOR THE ANALYSIS OF NONLOCAL EVOLUTION EQUATIONS, SIAM J. Math. Anal. 47 (2015), no. 2, 1330--1354, PDF

17. C. Cazacu, Controllability of the heat equation with an inverse-square potential localized on the boundary, SIAM J. Control Optim. 52 (2014), no. 4, 2055–2089, PDF

18. Liviu I. Ignat, Ademir Pazoto, Large time behaviour for a nonlocal diffusion - convection equation related with the gas dynamics, Discrete Contin. Dyn. Syst. 34 (2014), no. 9, 3575–3589, PDF

19. Farhod Abdullayev, Marian Bocea, and Mihai Mihailescu, A variational characterization of the effective yield set for ionic polycrystals, Appl. Math. Optim. 69 (2014), no. 3, 487–503, PDF

20. Marica A., Zuazua E., Boundary stabilization of numerical approximations of the 1-d variable coefficients wave equation: A numerical viscosity approach, submitted, Optimization with PDE constraints, 285–324, Lect. Notes Comput. Sci. Eng., 101, Springer, Cham, 2014, PDF

21. Marica A., Zuazua E., Propagation of 1-d waves in regular discrete heterogeneous media: a Wigner measure approach, Found. Comput. Math. 15 (2015), no. 6, 1571--1636, PDF

22. Marica Aurora Mihaela, Ervedoza Sylvain, Zuazua Enrique, Numerical meshes ensuring uniform observability of one-dimensional waves: construction and analysis, IMA Journal of Numerical Analysis, (2016) 36, 503--542

23. C. Cazacu and David Krejcirik: The Hardy inequality and the heat equation with magnetic field in any dimension, Communications in partial differential equations, (2016), Vol. 41, No. 7, 1056–1088, PDF

24. C. Cazacu: New estimates for the Hardy constant of multipolar Schr\"odinger operators with boundary singularities, Commun. Contemp. Math, (2015), 1550093 (28 pages), PDF

25. M. Farcaseanu, Denisa Stancu-Dumitru, On the existence of solutions for a quasilinear elliptic equation involving a nonlocal term,

Electonic Journal of Differential Equations, Vol. 2015 (2015), No. 293, pp. 1–8. , PDF

26. N. Beli, L. Ignat, E. Zuazua, Dispersion for 1-d Scrodinger and wave equation with BV coefficients, in press, Annales of IHP, PDF

27. L. Ignat, A. Pozo, A semi-discrete large-time behavior preserving scheme for the augmented Burgers equation, PDF

28. C. Cazacu, L. I. Ignat, A. Pazoto, On the asymptotic behavior of a subcritical convection-diffusion equation with nonlocal diffusion, Submitted. PDF

Habilitation Theses

Mihailescu Mihai, The analysis of some PDEs and related problems, 24/07/2012, PDF

Liviu Ignat, 31/05/2031, Qualitative analysis of some differential equations, PDF, slides, PDF

PhD Theses

Denisa Stancu, Qualitative Methods in the Study of Nonlinear Elliptic Problems, 19/09/2012, PDF

Best thesis award, Univ. of Craiova, 2013, PDF

Cristi Cazacu, HARDY INEQUALITIES, CONTROL AND NUMERICS FOR SINGULAR PDEs, PDF

Workshops/Conferences organized

1. Special Session on Applied Analysis, AMS Western Section Meeting, October 22-23, 2011, University of Utah, Salt Lake City, Utah, USA (http://www.ams.org/meetings/sectional/2184_program_ss15.html).Organizers: *Marian Bocea (Loyola University, Chicago, mbocea@luc.edu), Liviu , Mihai Mihailescu (University of Craiova & IMAR).

2 .Workshop for Young Researchers in Mathematics, Constanța, May 10 - May 11, 2012,

3. Workshop for Young Researchers in Mathematics, Constanța, May 09 - May 10, 2013,

4 . Special Session: Calculus of Variations and Partial Differential Equations, Joint International Meeting of the AMS and the Romanian Mathematical Society, Organizers: *Marian Bocea (Loyola University, Chicago, mbocea@luc.edu), Liviu Ignat (Institute of Mathematics of the Romanian Academy), Mihai Mihailescu (University of Craiova & IMAR), Daniel Onofrei (University of Houston)

5. Workshop for Young Researchers in Mathematics, May 22- May 23, 2014

6. WORKSHOP FOR YOUNG RESEARCHERS IN MATHEMATICS, May 21-24, 2015

7. Section "Analysis, PDE's & Applied Mathematics" of "Workshop for Young Researchers in Mathematics", 6th Edition, May 21-24, Constanta.

8. Coorganizer of the section "Analyse et controle des EDP" at XIII-eme Colloque Franco-Roumain de Mathematiques Appliquee, 25-29 August 2016, Iasi

Foreign experts that visited us

1. Julio Rossi in 2013, 2016, Universidad de Buenos Aires & Universidad de Alicante
2. Maria Teresa Perez in 2013, Universidad Autonoma de Madrid
3. Enrique Zuazua in 2013, 2014, Basque Center for Applied Mathematics
4. Florica Cirstea, 2013, University of Sydney
5. Diana Stan, 2012, 2013, 2014, 2015 Universidad Autonoma de Madrid
6. Steven H. Weintraub, 2012, Lehigh University, USA
7. Francisco De La Hoz Mendez 2012, University of the Basque Country, Spain
8. Daria Ghilli 2012, University of Padova, Italy
9. Alejandro Pozo, 2014, Basque Center for Applied Mathematics, Spain
10. Ademir Pazoto, 2014, 2015, 2016, Universidad Federal de Rio de Janeiro, Brasil
11. Traian Pirvu, 2015, McMaster University, Canda
12. Adina Rilea Ciomaga, 2015, Univ. Paris Diderot, France
13. Titus Hilberdink, University of Reading, 2016, UK
14. Nikolaos Diamantis, Univ. Nottingham, 2016, UK
15. Cristian Popescu, U.C. San Diego, 20-23/08/2016, USA
16. Gergely Harcos, Alfred Rényi Institute of Mathematics, 2016, Hungary

Talks 2016

1. A. Grecu, Dispersive Properties of the Solution for the Schrödinger Equation on a Graph with Cycle, Workshop for Young Researchers in Mathematics, 6th Edition, May 19th-22nd, 2016, Constanta, Romania

2. A. Marica, Wave propagation on irregular grids, Workshop for Young Researchers in Mathematics, 6th editions, Universitatea Ovidius din Constanta, 19-22 may 2016

3. A. Marica, Wave propagation on irregular grids}, XIII-eme Colloque Franco-Roumain de Mathematiques Appliquees, Universitatea Alexandru Ioan Cuza, Iasi, 25-29 August 2016.

4. L. Ignat, Dispersion property for Schr\"odinger equations, International Center for Advanced Studies, Buenos Aires, 26/04/2016

5. L. Ignat, Long-time behaviour for nonlocal convection-diffusion problems, 3rd Conference on Nonlocal Operators and Partial Differential Equations, 27.06.2016 - 01.07.2016, Bedlewo, Poland

6. L. Ignat, Dispersion property for Schr\"dinger equations, Workshop on geometry and PDEs, 10-11 June 2016, West University of Timişoara, Romania 2016

7. C. Cazacu, Controllability results for a Kuramoto-Sivashinsky model on trees, XIII-eme

Colloque Franco-Roumain de Mathematiques Appliquees, Iasi, Romania, 25/08/2016.

8. C. Cazacu, Decay rates for the heat evolution of the magnetic Laplacian with Hardy potential, Workshop for Young Researchers in Mathematics-6th edition, Constanta, Romania, 21/05/2016.

9. C. Cazacu, Asymptotic properties for a nonlocal diffusion problem with subcritical local convective term, Analysis and PDEs Seminar, University of Rio de Jaineiro, 21st September 2016

10. L. Marcoci, About factorization of some spaces of functions, Workshop for Young Researchers in Mathematics, 6th Edition, May 19th-22nd, 2016, Constanta, Romania

11. J. Rossi, Nonlocal perimeter, curvature and minimal surfaces for measurable sets, 6/07/2016, IMAR, Bucharest

12. Titus Hilberdink, Singular values of multiplicative Toeplitz matrices, 19/07/2016, IMAR, Bucharest

Talks 2015

1. A. Grecu, Heat and Schr\"odinger Kernels on Graphs with Cycles, Workshop for Young Researchers in Mathematics, May 21st-24th, 2015, 5th Edition, Constanta, Romania

2. L. Ignat, Long-time behaviour for nonlocal problems,17 April, 2015, San Juan, University of Puerto Rico, USAL. Ignat, Dispersive properties for Schr\"odinger equations, 24 April, 2015, San Juan, University of Puerto Rico, USA

3. L. Ignat, Dispersive properties for Schr\"odinger equations, The Eighth Congress of Romanian Mathematicians, June 26th-July 1st, 2015, Iasi, Romania

4. L. Ignat, Dispersion property for Schrodinger equations, 11 November 2015, IMAR, Bucharest

5. C. Cazacu, Asymptotic behavior for the heat equation with magnetic field and Hardy potential, Workshop in Partial Differential Equations, Optimal Design and Numerics, Benasque, Spain, 31/08/2015.

6. C. Cazacu, Optimal Hardy constants for Schr\"{o}dinger operators with multi-singular inverse-square potentials}, The Eighth Congress of Romanian Mathematicians, University of Iasi, Romania, 30/06/2015.

7. C. Bereanu, Prescribed mean curvature of manifolds in Minkowski space, Workshop for Young Researchers in Mathematics, May 21st-24th, 2015, 5th Edition, Constanta, Romania

8. I. Cimpean, A new approach to existence of invariant measure for Markovian semigroups, Workshop for Young Researchers in Mathematics, May 21st-24th, 2015, 5th Edition, Constanta, Romania

9. Adina Ralea Ciomaga, Stochastic homogenization of interfaces moving with changing sign velocity, IMAR, 20/11/2015

10. Traian Pirvu, "Stochastic calculus for finance", graduate course, IMAR, 10-12/2015

Talks 2014

(1) L. Ignat, Long-time behavior for nonlocal problems, Workshop for Young Researchers in Mathematics, University of Constanta, Romania, 22/05/2014

(2) L. Ignat, About nonlocal evolution equations, Meeting MTM, BCAM-Basque Center for Applied Mathematics, Bilbao, Spain, 13/06/2014.

(3) L. Ignat, Long-time behaviour for a nonlocal convection-diffusion equation, Universite de Evry, 05/06/2014

(4) L. Ignat, About Schr ̈odinger equations, Conferinta lunara a departamentului de ma- tematica al Universitatii Bucuresti, 3/04/2014

(5) L. Ignat, Long-time behaviour for nonlocal problems, The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications, July 07 - July 11, 2014, Madrid, Spain

(6) L. Ignat, Long-time behaviour for nonlocal problems, 12e Colloque Franco-Roumain de Mathmatiques Appliques, August 25-30, 2014, l’Universit de Lyon, Lyon, France.

(7) C. Cazacu, About the Hardy inequality and its applications to the asymptotic be- havior of parabolic equations II, Potential Theory Seminar, University of Bucharest, Romania, 11/11/2014.

(8) C. Cazacu, About the Hardy inequality and its applications to the asymptotic be- havior, 04/11/2014 of parabolic equations I, Potential Theory Seminar, University of Bucharest, Romania.

(9) C. Cazacu, Multipolar Hardy inequality with boundary singularities, Meeting MTM, BCAM-Basque Center for Applied Mathematics, Bilbao, Spain, 13/06/2014.

(10) C. Cazacu, New estimates for the best constant of a Hardy-type inequality with multi- singular potentials, Workshop for Young Researchers in Mathematics, University of Constanta, Romania, 22/05/2014.

(11) Denisa Stancu-Dumitru, The Asymptotic Behavior of Solutions to Nonhomogene- ous Eigenvalue Problems in Orlicz Sobolev Spaces, Workshop for Young Researchers in Mathematics, May 22-23, 2014, ”Ovidius” University of Constan?a, Constan?a, Romnia.

(12) Denisa Stancu-Dumitru, The limiting behavior of solutions to inhomogeneous eigen- values problems in Orlicz-Sobolev spaces, 12e Colloque Franco-Roumain de Mathma- tiques Appliques, August 25-30, 2014, l’Universit de Lyon, Lyon, France.

(13) Aurora Marica, Design of non-uniform meshes with uniform observability properties for 1-d waves, Conference on Mathematics and Its Applications, Kuwait, November 14-17, 2014

(14) Aurora Marica, Wave propagation on non-uniform meshes, The Third BCAM Work- shop on Computational Mathematics, talk , BCAM, Bilbao, July 17- 18, 2014

(15) Aurora Marica, Wave propagation on non-uniform meshes: uniform propagation/control properties, MTM Workshop, BCAM, Bilbao, June 12-13, 2014

(16) Aurora Marica, Well-posedness and control for models with discontinuous nonlineari- ties appearing in cardiology, Workshop New trends in modeling, control and inverse problems, Institut de Mathmatiques de Toulouse, poster , June 16-19, 2014.

Talks 2013

1. C. Cazacu, "On the first eigenvalue of a degenerate Sturm-Liouville problem", Workshop for Young Researchers in Mathematics, University of Constanta, Romania, 9 May, 2013.

2. C. Cazacu, "On Hardy inequalities", Department of Mathematics, University of Sussex, Brighton, UK, 28 February, 2013.

3. C. Cazacu, "Controllability of the heat equation with an inverse-square potential localized on the boundary", Workshop MTM, Bilbao, Spain, 18 February, 2013.

4. A. Marica, "Wave propagation on non-uniform media", University of Zagreb, January 24 2013.

5. A. Marica, "Propagation and stabilization properties of waves on discrete heterogeneous media", Workshop MTM, February 18-19 2013.

6. A. Marica, "Uniform observability properties for discrete waves on non-uniform concave meshes", Workshop for Young Researchers in Mathematics, Constanta, May 9 - 10 2013.

7. M. Mihailescu, "The asymptotic behavior of some power-law functionals in Sobolev spaces with variable exponents", Advances in Differential Equations: symmetrizations and related topics, March 14-15, 2013, Babes-Bolyai University, Cluj-Napoca, Romania

8. L. Ignat, "Nonlocal evolution equations", MTM Worshop, Basque Center for Applied Mathematics, 18th February, Bilbao, 2013

9. L. Ignat, "Dispersion for Schrödinger equations", Pde's, Dispersion, Scattering theory and Control theory, Monastir, 10-14 June 2013

10. L. Ignat, "Long-time behaviour for a nonlocal convection-diffusion equation", AMS Meeting, Alba Iulia, June 27 - 30, 2013

11. D. Stancu-Dumitru, “PDE’s involving an anisotropic operator with variable exponents ”, Workshop for Young Researchers in Mathematics, May 9-10, 2013, “Ovidius” University of Constanta, Constanta, Romania.

12. D. Stancu-Dumitru, “Anisotropic Variable Exponent PDEs”, Joint International Meeting of the AMS and the Romanian Mathematical Society, Special session: Calculus of Variations and Partial Differential Equations, June 27-30, 2013, “1 Decembrie 1918” University of Alba Iulia, Alba-Iulia, Romania.

13. Mihai Mihailescu, "PDE’s involving a variable exponent Grushin-type operator", Joint International Meeting of the AMS and the Romanian Mathematical Society, June 27-30, 2013, 1 Decembrie 1918 University, Alba Iulia, Romania

Talks 2012

(1) Liviu Ignat, \Dispersive properties for Schrodinger equations" la Universitatea din

Craiova, 6/09/2012.

(2) Liviu Ignat, \Dispersive properties for Schrodinger equations", Universit.e d'Evry,

Frant.a, 21/06/2012.

(3) Liviu Ignat, Dispersive properties for Schrodinger equations, \XI.eme Colloque Franco-

Roumain de Mathematiques Appliqu.ees", Bucure.sti, Rom^ania, August, 2012.

(4) Liviu Ignat, Nonlocal evolution equations, \XI.eme Colloque Franco-Roumain de Math.e-

matiques Appliqu.ees", Bucure.sti, Rom^ania, August, 2012.

(5) Cristian Cazacu, \Teoria controlului .si aplicat.ii" la \A XVI-a Conferint..a anual.a a

Societ.at.ii de S.tiin.se Matematice din Rom^ania", Ploie.sti, 20 Octombrie, 2012.

(6) Cristian Cazacu, \Controllability of the wave equation with a quadratic singular

potential localized on the boundary" la\XI.eme Colloque Franco-Roumain de Math.

App., Bucure.sti, 27 August, 2012.

(7) Cristian Cazacu, \Numerical methods for Schrodinger operators with inverse squ-

are potentials" in \Aquitaine-Euskadi Workshop on Applied Mathematics", Bilbao,

Spania, 7 Iunie, 2012.

(8) Cristian Cazacu, \Optimal constants in multipolar Hardy Inequalities" in \Workshop

for Young Researchers in Mathematics", Constant.a, Rom^ania, 11 Mai, 2012.

(9) Cristian Cazacu, \Finite-Element approaches for Schrodinger operators with inverse

square potentials", la \Basque / Hungarian Workshop on Numerical Methods for

Large Systems", Bilbao, Spania, 26 Aprilie, 2012.

(10) Mihai Mihailescu, Remarks on the .rst eigenvalue of the p(x)-Laplace operator, Se-

minar of the PDE's Research Group from Basque Center of Applied Mathematics,

Bilbao, Spania, 14 Februarie, 2012.

(11) Mihai Mihailescu, A maximum principle related with eigenvalue problems involving

variable exponents, Workshop for Young Researchers in Mathematics, 2012, "Ovidius"

University of Constant.a, Constant.a, 10-11 Mai, 2012.

(12) Denisa Stancu, On some PDEs involving a variable exponent Grushin- type operator,

Workshop for Young Researchers in Mathematics, Ovidius University of Constanta,

Constant.a, Rom^ania, 10-11 Mai, 2012.

(13) Denisa Stancu, A variable exponent Grushin-type operator and applications to PDEs,

\XI.eme Colloque Franco-Roumain de Math.e-matiques Appliqu.ees", University of Bu-

charest, Bucure.sti, Rom^ania, 24-30 August, 2012.

(14) Denisa Stancu, Some Anisotropic Variable Exponent PDEs, Seminar of the PDEs

Research Group from Basque Center for Applied Mathematics, Bilbao, Spania, 17

Octombrie, 2012.

(15) Aurora Marica, Wave propagation in discrete heterogeneous media, Workshop of the

ESF project "Optimization with PDE constraints", Charles University, Praga, Cehia,

9-10/12/2011.

(16) Aurora Marica, Some sophisticated numerical approximations for waves: propagation,

observability, dispersion and control, "Basque-Hungarian Workshop on Numerical Me-

thods for Large Systems", BCAM, Bilbao, 26/04/2012.

(17) Aurora Marica, Wave propagation in non-uniform meshes: a Wigner measure approach,

"Workshop for Young Researchers in Mathematics", Ovidius University, Constant.a,

10/05/2011.

(18) Aurora Marica, High frequency wave propagation on non-uniform meshes, "EFEF2012

- European .nite element fair", BCAM, Bilbao, Spania, 08-09/06/2012.

(19) Aurora Marica, Poster: Wave propagation in discrete heterogeneous media, "14-th In-

ternational conference on hyperbolic problems: theory, numerics, applications", Uni-

versit.a degli Studi di Padova, Italia, 25-29/06/2012.

(20) Aurora Marica, High frequency wave propagation in non-uniform meshes, "XI.eme

Colloque Franco-Roumain de Math.ematiques Appliqu.ees", Facultatea de Matematic.a-

Informatic.a a Universit.at.ii din Bucure.sti, 24-30/08/2012.

(21) Aurora Marica, High frequency wave propagation in non-uniform meshes, "3-.eme

Conf.erence Internationale de la Soci.et.e Marocaine de Math.ematiques Appliqu.ees

(SM2A)", Marrakech, Maroc, 10-13/09/2012.

(22)Daria Ghili, Stability of isoperimetric inequalities for Monge-Amp‘ere functionals, University of Florence, Italy, Workshop for Young Researchers in Mathematics, 2012, ”Ovidius” University of Constan ̧ta, Constan ̧ta, 10-11 Mai, 2012.

(23) Francisco DE LA HOZ MENDEZ, Singularities in Fluid Dynamics University of the Basque Country, Spain, Workshop for Young Researchers in Mathematics, 2012, ”Ovi- dius” University of Constan ̧ta, Constan ̧ta, 10-11 Mai, 2012.

(24) Diana Stan, Le comportement asymptotique de l equation de di?usion nonlineare ut = ∆pu dans un domaine borne, Universidad Autonoma de Madrid, “XI`eme Colloque Franco-Roumain de Mathematiques Appliqu ́ees”, Bucure ̧sti, Romˆania, August, 2012

(25) Mihai Mihailescu, A maximum principle connected with eigenvalue problems involving variable exponents, Special Session on Applied Analysis, AMS Western Section Meeting, October 22-23, 2011, University of Utah, Salt Lake City, Utah, USA