Asymptotic behavior of solutions to semilinear wave equations with dissipative structure

Pages: 602 - 613, Issue Special, September 2007

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Hideo Kubo - Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan (email)

Abstract: We study the asymptotic behavior of solutions to semilinear wave equations. The aim of this note is to find a condition on the nonlinearity which guarantees that the corresponding equation has dissipative structure, and to show that asymptotic behavior of the global solution is possibly different from the free solution.

Keywords:  Asymptotic behavior, Dissipative structure, Wave equation.
Mathematics Subject Classification:  Primary: 35L70; Secondary: 35B40.

Received: September 2006;      Revised: August 2007;      Published: September 2007.