DECAY ESTIMATES FOR SOLUTIONS OF ABSTRACT WAVE EQUATIONS WITH GENERAL DAMPING FUNCTION

Abstrakt

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.

Klíčová slova

• Abstract wave equation
• convergence to equilibrium
• decay estimates
• Lojasiewicz inequality