TE 4/2010 Grant

Team

1. Liviu Ignat - principal investigator

2. Mihai Mihailescu - researcher

3. Cristian Bereanu - researcher

4. Cristian Gavruș - master student SNSB (now PhD student at University of Barkeley, California, USA)

Project abstract

This project is devoted to the analysis of PDE with emphasis on well-posedness, numerical approximation of the solutions and their asymptotic behaviour.

There are few themes

1. Numerical approximations of dispersive equations: discret Schr\"odinger like equations

2. Asymptotic properties of nonlocal diffusion equations. We analysis the decay of the solutions and their profile when the time become large.

3. Equations on networks: continuous or discrete equations, Schr\"odinger like equations

Papers

OBS: the articles are in preprint version. For the final version you need institutional acces.

1. LIVIU I. IGNAT, DAMIAN PINASCO, JULIO D. ROSSI AND ANGEL SAN ANTOLIN, DECAY ESTIMATES FOR NONLINEAR NONLOCAL DIFFUSION PROBLEMS IN THE WHOLE SPACE, PDF, accepted to Journal d'Analyse Mathematique

2. L. Ignat, J. D. Rossi, A. San Antolin, Lower and upper bounds for the first eigenvalue of nonlocal

diffusion problems in the whole space, Journal of Differential Equations, Volume 252, Issue 12, 15 June 2012, Pages 6429-6447, PDF

3. L.I. Ignat, D. Stan, Dispersive properties for discrete Schrodinger equations, JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS

Volume 17, Number 5, 1035-1065, PDF

4. L. I. Ignat, A SPLITTING METHOD FOR THE NONLINEAR SCHRODINGER EQUATION, J. Differential Equations 250 (2011) 3022–3046, PDF

5. Mihai Mihăilescu, Csaba Varga, Multiplicity results for some elliptic problems with nonlinear boundary conditions involving variable exponents, Computers and Mathematics with Applications 62 (2011) 3464–3471

6. Cristian Bereanu, Petru Jebelean, Jean Mawhin, Multiple solutions for Neumann and periodic problems with singular φ-Laplacian, Journal of Functional Analysis 261 (2011) 3226–3246

7. L. I. Ignat, Strichartz estimates for the Schrodinger equation on a tree and applications, SIAM J. Math. Analysis., Vol. 42, No. 5, pp. 2041–2057, PDF

8. A. Kristaly, M. Mihailescu, V. Radulescu, S. Tersian, Spectral estimates for a nonhomogeneous difference problem, Communications in Contemporary Mathematics, Vol. 12, No. 6 (2010) 1--14. PDF

Talk given by Cristian Gavrus at BCAM, april 2012, PDF

Master Thesis by Cristian Gavrus at SNSB, June 15, 2012, PDF

Workshops 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).

2. Workshop for Young Researchers in Mathematics, Constanța 12-13 mai 2011

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

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

5. 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), Daniel Onofrei (University of Houston)

6. "Workshop on Partial Differential Equations".

Foreign experts that visited us

1. Julio Rossi in 2011, 2013, Universidad de Buenos Aires & Universidad de Alicante

2. Maria Teresa Perez in 2011, 2013, Universidad Autonoma de Madrid

3. Enrique Zuazua in 2011, 2013, Basque Center for Applied Mathematics

4. Florica Cirstea, 2013, University of Sydney

5. Diana Stan, 2011, 2012, 2013, Universidad Autonoma de Madrid