L^p-asymptotic stability analysis of a 1D wave equation with a nonlinear damping

This paper is concerned with the asymptotic stability analysis of a one dimensional wave equation with Dirichlet boundary conditions subject to a nonlinear distributed damping with an L p functional framework, p \(\in\) [2, \(\infty\)]. Some well-posedness results are provided together with exponent...

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Bibliographic Details
Published inarXiv.org
Main Authors Chitour, Yacine, Marx, Swann, Prieur, Christophe
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 26.07.2019
Subjects
Asymptotic properties
Boundary conditions
Damping
Decay rate
Dimensional stability
Dirichlet problem
Nonlinear programming
Stability analysis
Trajectory analysis
Wave equations
Well posed problems
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ISSN2331-8422

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Summary:This paper is concerned with the asymptotic stability analysis of a one dimensional wave equation with Dirichlet boundary conditions subject to a nonlinear distributed damping with an L p functional framework, p \(\in\) [2, \(\infty\)]. Some well-posedness results are provided together with exponential decay to zero of trajectories, with an estimation of the decay rate. The well-posedness results are proved by considering an appropriate functional of the energy in the desired functional spaces introduced by Haraux in [11]. Asymptotic behavior analysis is based on an attractivity result on a trajectory of an infinite-dimensional linear time-varying system with a special structure, which relies on the introduction of a suitable Lyapunov functional. Note that some of the results of this paper apply for a large class of nonmonotone dampings.
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SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
ISSN:2331-8422