Asymptotic regularity of solutions of a nonautonomous damped wave equation with a critical growth exponent

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December 2004, 3(4): 921-934. doi: 10.3934/cpaa.2004.3.921

Asymptotic regularity of solutions of a nonautonomous damped wave equation with a critical growth exponent

1.	Institute of Information Transmission Problems, Russian Academy of Sciences, Bol’shoi Karetnyi 19, 127994, GSP-4, Moscow, Russian Federation

Received December 2003 Revised June 2004 Published September 2004

Abstract
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The paper is devoted to study of the longtime behavior of solutions of a damped semilinear wave equation in a bounded smooth domain of $\mathbb R^3$ with the nonautonomous external forces and with the critical cubic growth rate of the nonlinearity. In contrast to the previous papers, we prove the dissipativity of this equation in higher energy spaces $E^\alpha$, $0<\alpha\le 1$, without the usage of the dissipation integral (which is infinite in our case).

Keywords: nonautonomous attractors, Damped wave equations, critical growth rate, regularity of attractors..

Mathematics Subject Classification: Primary 37B40, 37B45.

Citation: Sergey Zelik. Asymptotic regularity of solutions of a nonautonomous damped wave equation with a critical growth exponent. Communications on Pure & Applied Analysis, 2004, 3 (4) : 921-934. doi: 10.3934/cpaa.2004.3.921

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