# American Institute of Mathematical Sciences

November  2018, 38(11): 5921-5941. doi: 10.3934/dcds.2018257

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

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

Received  April 2018 Published  August 2018

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.

Citation: Montgomery Taylor. The diffusion phenomenon for damped wave equations with space-time dependent coefficients. Discrete & Continuous Dynamical Systems, 2018, 38 (11) : 5921-5941. doi: 10.3934/dcds.2018257
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##### References:
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