# News

09.11.2017 - Diffusion phenomena for wave equation with space-dependent damping term

Mercoledì 15 novembre alle ore 15:00, in aula seminari, il Dott. Motohiro Sobajima dal Dipartimento di Matematica dell'Università delle Scienze di Tokyo terrà un seminario dal titolo:

"Diffusion phenomena for wave equation with space-dependent damping term".

Abstract
In this talk we consider the wave equation with damping term u_tt-\Delta u+ a(x)u_t=0 with suitable initial data. If a(x)=1, it is known that the solution of this equation behaves like the one of heat equation for
sufficiently large t.
In this talk we show that even if a(x) \approx |x|^{-\alpha} (0 <\alpha <1), the behavior of solution is given by the one ofu_t=a(x)^{-1}\Delta u.
In the proof L^p-L^q type estimates for semigroup by a(x)^{-1}\Delta is used. This is based on the joint work with Prof. Yuta Wakasugi (Ehime University).

Referente Prof. Giorgio Metafune