## 偏微分方程式セミナー(2016/4/22): Asymptotics for Linear Dissipative Wave Equations, Borislav Yordanov氏（北海道大学）

2016年 　 4月 22日 16時 30分 ～ 2016年 　 4月 22日 17時 30分

Borislav Yordanov氏（北海道大学）

The solutions of dissipative wave equations have relatively simple behavior as time goes to infinity: the leading terms are proportional to a Gaussian or, more generally, to a solution of the corresponding diffusion equation.
That second-order time derivatives are negligible in the long-time asymptotics of such equations is known as the diffusion phenomenon" for damped waves. We discuss two methods for showing the diffusion phenomenon: weighted energy method and spectral method.

We also give applications to $L^p$-estimates for dissipative wave equations with variable coefficients generalizing the classical estimates of A. Matsumura in On the asymptotic behavior of solutions of semi-linear wave equations", Publ. Res. Inst. Math. Sci., Kyoto Univ., 12 (1976), 169-189.