Seminár z kvalitatívnej teórie diferenciálnych rovníc

Seminar on Qualitative Theory of Differential Equations

Thursday 19.5.2016 at 14:00 Lecture room M-223

Tatsuki Kawakami (Osaka Prefecture University a Universita degli Studi di Milano):

Higher order asymptotic expansions to the solutions for a nonlinear damped wave equation

Abstract:

We study the Cauchy problem for a nonlinear damped wave equation.

Under suitable assumptions for the nonlinearity and the initial data,

we obtain the global solution which satisfies weighted estimates.

Furthermore, we establish the higher order asymptotic expansion of the solution.

Our proof is based on the approximation formula of the linear solution

and the nonlinear approximation theory for a nonlinear parabolic equation.

This talk is based on a joint work with Hiroshi Takeda (Fukuoka Institute of Technology).