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

20191025 16:30 
20191025 18:00
 Place
 Faculty of Science Building #3, Room 309

Speaker/Organizer
 Motohiro Sobajima (Tokyo University of Science)

 In this talk we consider the semilinear damped wave equation $u_{tt}\Delta u+u_t=u^{p1}u$ in an exterior domain, where $1 < p < N/(N2)$. 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 (HayashiKaikinaNaumkin(2004), IkedaInuiWakasugi(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 SobajimaWakasugi(2019,CCM).