CONVERGENCE TO EQUILIBRIUM OF RELATIVELY COMPACT SOLUTIONS TO EVOLUTION EQUATIONS

Abstract

We prove convergence to equilibrium for relatively compact solutions to an abstract evolution equation satisfying energy estimates near the omega-limit set. These energy estimates generalize Lojasiewicz and Kurdyka-Lojasiewicz-Simon gradient inequalities.

We apply the abstract results to several ODEs and PDEs of first and second order.

Keywords

• Convergence to equilibrium
• gradient system
• Kurdyka-Lojasiewicz gradient inequality
• gradient-like system