Electron. J. Differential Equations, Vol. 2016 (2016), No. 334, pp. 1-17.

Decay estimates for solutions of abstract wave equations with general damping function

Tomas Barta

Abstract:
In this article we prove convergence to equilibrium and decay estimates for a class of damped abstract wave equations. We focus on the damping term to be as general as possible, including functions that oscillate between two positive functions in a neighborhood of the origin and/or behave differently in each direction.

Submitted March 13, 2016. Published December 28, 2016.
Math Subject Classifications: 35L90, 35L10, 37L15.
Key Words: Abstract wave equation; convergence to equilibrium; decay estimates; Lojasiewicz inequality.

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Tomas Barta
Department of Mathematical Analysis
Faculty of Mathematics and Physics
Charles University in Prague
Sokolovska 83, 18675 Praha 8, Czech Republic
email: Tomas.Barta@mff.cuni.cz

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