# American Institute of Mathematical Sciences

April  1996, 2(2): 173-190. doi: 10.3934/dcds.1996.2.173

## On the critical decay and power for semilinear wave equtions in odd space dimensions

 1 Department of Mathematics, Hokkaido University, Sapporo 060, Japan

Received  September 1995 Published  February 1996

In this paper we study global behaviors of solutions of initial value problem to wave equations with power nonlinearity. We shall derive space-time decay estimates according to decay rates of the initial data with low regularity (in classical sense). Indeed we can control $L^\infty$-norm of a solution in high dimension, provided the initial data are radially symmetric. This enables us to construct a global solution under suitable assumptions and to obtain an optimal estimate for a lifespan of a local solution.
Citation: Hideo Kubo. On the critical decay and power for semilinear wave equtions in odd space dimensions. Discrete & Continuous Dynamical Systems - A, 1996, 2 (2) : 173-190. doi: 10.3934/dcds.1996.2.173
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