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Uniform inertial sets for damped wave equations

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  • In this paper, we establish the existence of inertial sets for a class of wave equations in which the coefficient of the second order time derivative is $\varepsilon$. We show that the fractal dimension of these inertial sets does not depend on $\varepsilon$ for $\varepsilon$ small enough. We then compare the asymptotic behavior of the problem (as $\varepsilon\to 0$) through a continuity like property of the inertial sets. The autonomous case and nonautonomous case are studied.
    Mathematics Subject Classification: 35B40, 35B45, 35L05.


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