Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

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

Pages: 173 - 190, Volume 2, Issue 2, April 1996      doi:10.3934/dcds.1996.2.173

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Hideo Kubo - Department of Mathematics, Hokkaido University, Sapporo 060, Japan (email)

Abstract: 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.

Keywords:  semilinear wave equtions, critical decay, global behavior.
Mathematics Subject Classification:  35L05,35L70.

Received: September 1995;      Available Online: February 1996.