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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

Akisato Kubo 1,

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

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