Establishes L^p well-posedness and exponential asymptotic stability for the 1D wave equation with nonlinear damping using energy functionals and a Lyapunov-based attractivity result on a linear time-varying system.
Stability analysis of dissipative systems subject to nonlinear damping via Lyapunov techniques
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abstract
In this article, we provide a general strategy based on Lyapunov functionals to analyse global asymptotic stability of linear infinite-dimensional systems subject to nonlinear dampings under the assumption that the origin of the system is globally asymp-totically stable with a linear damping. To do so, we first characterize, in terms of Lyapunov functionals, several types of asymptotic stability for linear infinite-dimensional systems, namely the exponential and the polynomial stability. Then, we derive a Lyapunov functional for the nonlinear system, which is the sum of a Lyapunov functional coming from the linear system and another term with compensates the nonlinearity. Our results are then applied to the linearized Korteweg-de Vries equation and some wave equations.
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math.AP 1years
2019 1verdicts
UNVERDICTED 1representative citing papers
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L^p-asymptotic stability analysis of a 1D wave equation with a nonlinear damping
Establishes L^p well-posedness and exponential asymptotic stability for the 1D wave equation with nonlinear damping using energy functionals and a Lyapunov-based attractivity result on a linear time-varying system.