The diffusion phenomenon for damped wave equations with space-time dependent coefficients

Montgomery Taylor

doi:10.3934/dcds.2018257

Article Contents

2018, Volume 38, Issue 11: 5921-5941. Doi: 10.3934/dcds.2018257

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The diffusion phenomenon for damped wave equations with space-time dependent coefficients

Montgomery Taylor

Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA

Received: April 2018

Published online: November 2018

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Abstract

We introduce a method to study the long-time behavior of solutions to damped wave equations, where the coefficients of the equations are space-time dependent. We show that solutions exhibit the diffusion phenomenon, connecting their asymptotic behaviors with the asymptotic behaviors of solutions to corresponding parabolic equations. Sharp decay estimates for solutions to damped wave equations are given, and decay estimates for derivatives of solutions are also discussed.

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Mathematics Subject Classification: Primary: 35L15; Secondary: 35B40.

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References

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