偏微分方程式セミナー: Semilinear damped wave equation with slowly decaying initial data in exterior domain, 側島 基宏 氏

開催日時

2019年10月25日 16時 30分 ～ 2019年10月25日 18時 00分

場所

北海道大学理学部3号館3-309室

講演者

側島 基宏 氏 (東京理科大学)

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).

世話人：黒田 紘敏、浜向 直