Display Abstract

Title Semi-linear structurally damped evolution models

Name Michael Reissig
Country Germany
Email reissig@math.tu-freiberg.de
Co-Author(s) Pham Trieu Duong, Marcello D'Abbicco
Submit Time 2014-02-07 07:18:30
Special Session 60: Recent advances in evolutionary equations
The goal of the lecture is to study the Cauchy problem for structurally damped $\sigma$-evolution models u_{tt} + (-\Delta)^\sigma u + (-\Delta}^\delta u_t=f(u,u_t,|D|^\alpha u),\,\,u(0,x)=u_0(x),\,\,u_t(0,x)=u_1(x) , where $\sigma \geq 1$, $\delta \in (0,\sigma]$ and $\alpha \in [0,\sigma]$. Our main issue is the global existence (in time) of small data solutions. It is related to determine the critical exponent (of Fujita type). The considerations base on a very precise linear theory. The main tool are Strichartz decay estimates not necessarily on the conjugate line.