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

Sergey Zelik

doi:10.3934/cpaa.2004.3.921

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2004, Volume 3, Issue 4: 921-934. Doi: 10.3934/cpaa.2004.3.921

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

Sergey Zelik^1,

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

Received: November 30, 2003

Revised: May 31, 2004

Published: November 2004

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Abstract

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).

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Mathematics Subject Classification: Primary 37B40, 37B45.

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

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