Large time behavior of nonlocal diffusion equations in R^N // Multiplicity of ground state solutions for a semilinear equation

Speaker:  Noemí Wolanski (U. Buenos Aires) // Carmen Cortázar (PUC, Chile) ()
Date:  Friday, 05 May 2023 - 13:00
Place:  Aula Naranja, ICMAT



12:30.  ☕Coffee Break☕

13:00. " Large time behavior of nonlocal diffusion equations in \(\mathbb R^N\)", Noemí Wolanski (U. Buenos Aires)

Abstract: I will start by revisiting classical results on asymptotic simplification, in particular for the classical heat equation —the best known case. Then, I will present some results recently obtained for the case in which the classical time derivative is replaced by a fractional one. These are good models for diffusion in materials with memory and/or for diffusion in sticking materials. Our results are surprising in several ways when compared with the classical ones. These first results correspond to the Cauchy problem —null second member in the equation. Finally, I will  discuss the inhomogeneous case both for the fractional time derivative as well as the classical time derivative, as we have obtained surprising new results even in this latter case.
This work has been done in collaboration with Carmen Cortázar from Universidad Católica de Chile and Fernando Quirós from Universidad Autónoma de Madrid.

13:45. "Multiplicity of ground state solutions for a semilinear equation", Carmen Cortázar (PUC, Chile)

Abstract: Given a number \(k\), we want functions  \(f\) so that the problem \(\Delta u + f(u) = 0\) has at least \(k\)  ground states.
This is done by having abrupt but controlled magnitude changes on \(f\).