Our PDE Seminar

For our PDE seminar history visit this link :https://sites.google.com/site/liviuignat/seminar

Talks

  • Rajae Bentahar (Université Abdelmalek Essaadi, Ecole Nationale des Sciences Appliquées (ENSA), Tetouan, Maroc)

Coordinates: FMI-UB & IMAR (online talk), November 18, 2021, from 10:00-11:00 a.m. (local time in Bucharest, Romania)

Title of the talk: EXISTENCE OF RENORMALIZED SOLUTIONS FOR SOME NONCOERCIVE ANISOTROPIC ELLIPTIC PROBLEMS WITH NEUMANN BOUNDARY CONDITIONS.

Abstract: Our aim in this work is to prove the existence of at least one renormalized solution for an anisotropic elliptic problem with Neumann boundary conditions. Key words: Anisotropic Sobolev spaces, renormalized solution, elliptic problem, Neumann boundary conditions.


  • Alejandro Garriz Molina (Autonomous University of Madrid, Spain)

Coordinates: FMI-UB, November 25, 2019, from 3:00-4:00 pm, room 214 (Google)

Title of the talk: Coupling of Local and Non-local operators.

Abstract:

During this session we will see how the definition of an energy functional that is local in a domain and non-local in the complementary gives rise to a parabolic problem that shares this properties by coupling both operators, presenting results about existence and asymptotic behaviour of the solutions for the initial value problem, and convergence of the operator to the laplacian, for all three problems: Cauchy, Dirichlet and Neumann.We will put special attention to the tools used in this study, proposing new problems that can be studied in a similar way to ours and commenting on possible applications of the model.


  • Diana Stan (University of Cantabria, Santander, Spain),

Coordinates: FMI-UB, October 7, 2019, from 3:00-4:00 pm, room 215.

Title of the talk: Carleman estimates for fractional operators.

Abstract: Firstly, we consider changing-sign solutions to the heat equation for such operators. We prove monotonicity inequalities and convexity of certain energy functionals to deduce Carleman estimates with linear exponential weight. Our approach is based on spectral methods and functional calculus. Secondly, we use pseudo-differential calculus inorder to prove Carleman estimates with quadratic exponential weight, both in parabolic and elliptic contexts. The latter also holds in the case of the fractional Laplacian.

Joint work with Luz Roncal and Luis Vega. Partially supported by the ERCEA Advanced Grant 2014 669689-HADE. References: L Roncal, D Stan, L Vega, Carleman type inequalities for fractional relativistic operators. preprint arXiv:1909.10065