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In this article, we provide a general strategy based on Lyapunov functionalsto analyse global asymptotic stability of linear infinite-dimensional systemssubject to nonlinear dampings under the assumption that the origin of thesystem is globally asymp-totically stable with a linear damping. To do so, wefirst characterize, in terms of Lyapunov functionals, several types ofasymptotic stability for linear infinite-dimensional systems, namely theexponential and the polynomial stability. Then, we derive a Lyapunov functionalfor the nonlinear system, which is the sum of a Lyapunov functional coming fromthe linear system and another term with compensates the nonlinearity. Ourresults are then applied to the linearized Korteweg-de Vries equation and somewave equations.

Stability analysis of dissipative systems subject to nonlinear damping via Lyapunov techniques