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 exponential...
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| Main Authors | , , |
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| Format | Journal Article |
| Language | English |
| Published |
26.07.2019
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| Subjects | |
| Online Access | Get full text |
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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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| DOI: | 10.48550/arxiv.1907.11712 |