PDE Seminar (2019/10/25): Semilinear damped wave equation with slowly decaying initial data in exterior domain

2019-10-25 16:30 - 2019-10-25 18:00
Faculty of Science Building #3, Room 309
Motohiro Sobajima (Tokyo University of Science)
In this talk we consider the semilinear damped wave equation $u_{tt}-\Delta u+u_t=|u|^{p-1}u$ in an exterior domain, where $1 < p < N/(N-2)$. Here we deal with a class of initial data allowing polynomially decaying functions at spatial infinity. In the case of whole space $\mathbf{R}^N$, the Fourier analysis is valid well, then the global existence of solutions is known (Hayashi-Kaikina-Naumkin(2004), Ikeda-Inui-Wakasugi(2017)). In contrast, in the case of exterior domain, the behavior of solutions has not been well studied. To attack this problem, we use a weight energy method involving Kummer's hypergeometric functions which is discovered in Sobajima-Wakasugi(2019,CCM).