On the critical decay and power for semilinear wave equtions in odd space dimensions
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.
Received: September 1995; Published: February 1996.
2013 IF (1 year).923