Convergence and decay estimates for a class of second order dissipative equations involving a non-negative potential energy

Imen Ben Hassen (1) , Alain Haraux (2)

1 Département de Mathématiques
2 LJLL - Laboratoire Jacques-Louis Lions

\begin{abstract} We estimate the rate of decay of the difference between a solution and its limiting equilibrium for the following abstract second order problem \begin{equation*} \ddot{u}(t) + g(\dot{u}(t))+ \cM(u(t))=0,\quad t\in\R_+ , \end{equation*} where $\cM$ is the gradient operator of a non-negative functional and $g$ is a nonlinear damping operator, under some conditions relating the Lojasiewicz exponent of the functional and the growth of the damping around the origin. \end{abstract}

Domaines: Analyse numérique [cs.NA]

Imen Ben Hassen, Alain Haraux. Convergence and decay estimates for a class of second order dissipative equations involving a non-negative potential energy. 2010. ⟨hal-00520111⟩