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

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March 2004, 3(1): 59-74. doi: 10.3934/cpaa.2004.3.59

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

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

Received October 2002 Revised June 2003 Published January 2004

Abstract
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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 $.

Keywords: lower bounds, decay estimate, Euler-Poisson-Darboux equation, optimality..

Mathematics Subject Classification: 35L15, 35L20, 35L7.

Citation: Akisato Kubo. Asymptotic behavior of solutions of the mixed problem for semilinear hyperbolic equations. Communications on Pure & Applied Analysis, 2004, 3 (1) : 59-74. doi: 10.3934/cpaa.2004.3.59

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