Asymptotic behavior of solutions of the mixed problem for semilinear hyperbolic equations

Akisato Kubo

doi:10.3934/cpaa.2004.3.59

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2004, Volume 3, Issue 1: 59-74. Doi: 10.3934/cpaa.2004.3.59

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Asymptotic behavior of solutions of the mixed problem for semilinear hyperbolic equations

Akisato Kubo^1,

1.
Department of Mathematics, School of Health Sciences, Fujita Health University, Toyoake, Aichi 470-1192

Received: September 30, 2002

Revised: May 31, 2003

Published: February 2004

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Abstract

We discuss the optimality of the decay estimate of the mixed problem (MP) for semilinear hyperbolic equations of the type of the Euler-Poisson-Darboux equation. For this purpose we investigate decay properties and the lower bounds of the solutions to a boundary value problem related to (MP) as $t \rightarrow \infty $.

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Mathematics Subject Classification: 35L15, 35L20, 35L70.

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