PDE Seminar (2016/4/22): Asymptotics for Linear Dissipative Wave Equations, Borislav Yordanov （Hokkaido University）
 Date

2016422 16:30 
2016422 17:30
 Place
 Faculty of Science Building #3, Room 309

Speaker/Organizer
 Borislav Yordanov （Hokkaido University）

 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 secondorder time derivatives are negligible in the longtime 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 semilinear wave equations", Publ. Res. Inst. Math. Sci., Kyoto Univ., 12 (1976), 169189.