Seminar 4.4.2024: Jan Filo

[quittner]

Seminár z kvalitatívnej teórie diferenciálnych rovníc
Seminar on Qualitative Theory of Differential Equations

Thursday 4.4.2024 at 14:00 Lecture room F1-108

Ján Filo (KMANM FMFI UK):
Dvojne nelineárne difúzne rovnice v dvojkomponentnej oblasti

Abstract:
Let us consider a system of two double nonlinear diffusion equations
defined on two different components in the plane, that are connected
by a nonlinear contact condition. The system of two porous medium equations
defined on two different components of the real line, which are connected
by the nonlinear contact condition has already been studied in
[FP] J. Filo and V. Pluschke, The porous medium equation in a two-component
domain, J. Differential Equations 247 (2009) 2455-2484.

In the first part of my presentation, I am going to present a class
of explicit solutions of the power-like nonlinear diffusion equations
that are known as Barenblatt's solutions
and to show their qualitative properties.
Afterwards I shall speak about the results of [FP] and their
generalizations to two space dimensions and to more general
diffusion equations. Moreover, we present some numerical simulations
of the problem under consideration.

This is a joint work with Jela Babušíková and Patrik Mihala.