MAFIA - the seminar you can’t refuse
On June 13th, Liviu Ignat from the Institute of Mathematics of the Romanian Academy will talk about the Asymptotic behaviour of solutions for some diffusion problems on a metric graphs.
The seminar starts at noon in room T212 at Trojanova 13.
"In this talk, we present some recent results about the long-time behaviour of the solutions for some diffusion processes on a metric graph. We study evolution problems on a metric-connected finite graph in which some of the edges have infinity lengths.
We show that the asymptotic behaviour of the solutions of the heat equation (or even some nonlocal diffusion problems) is given by the solution of the heat equation, but on a star-shaped graph in which there is only one node and as many infinite edges as in the original graph. In this way, we obtain that the compact component that consists of all the vertices and all the edges of finite length can be reduced to a single point when looking at the asymptotic behaviour of the solutions.
We prove that when time is large the solution behaves like a Gaussian profile on the infinite edges.
When the nonlinear convective part is present, we obtain similar results but only on a star-shaped tree."