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 Title On diffusion phenomena for the linear wave equation with space-dependent damping
 Name Yuta Wakasugi Country Japan Email y-wakasugi@cr.math.sci.osaka-u.ac.jp Co-Author(s) Submit Time 2014-02-22 04:20:35 Session Special Session 60: Recent advances in evolutionary equations
 Contents We consider the diffusion phenomena for the linear wave equation with space-dependent damping. It is well known that if the damping term has a constant coefficient, then the solution behaves like that of the corresponding heat equation as time goes to infinity. On the other hand, it is also known that when the coefficient of the damping term decays sufficiently fast near infinity, the solution behaves like that of the free wave equation. In this talk, we consider the intermediate case, that is, the case where the coefficient of the damping term decays slowly near infinity, and we show that the asymptotic profile of the solution is given by a solution of the corresponding heat equation. This result corresponds to that of J. Wirth, who treated the time-dependent damping cases. The key point of the proof is weighted energy estimates for higher order derivatives, which are based on some recent results by G. Todorova, B. Yordanov, R. Ikehata and K. Nishihara.