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Well-posedness and exponential stability for a nonlinear wave equation with acoustic boundary conditions
  • George J. Bautista,
  • Juan Límaco,
  • Leyter Potenciano-Machado
George J. Bautista
Universidad Tecnologica de los Andes

Corresponding Author:[email protected]

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Juan Límaco
Universidade Federal Fluminense
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Leyter Potenciano-Machado
University of Jyäskylä
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In this paper, we prove the well-posedness of a nonlinear wave equation coupled with boundary conditions of Dirichlet and acoustic type imposed on disjoints open boundary subsets. The proposed nonlinear equation models small vertical vibrations of an elastic medium with weak internal damping and a general nonlinear term. We also prove the exponential decay of the energy associated with the problem. Our results extend the ones obtained by Frota-Goldstein [18] and Limaco-Clark-Frota-Medeiros [26] to allow weak internal dampings and removing the dimensional restriction 1≤ n≤4. The method we use is based on a finite-dimensional approach by combining the Faedo-Galerkin method with suitable energy estimates and multiplier techniques.
07 Feb 2023Submitted to Mathematical Methods in the Applied Sciences
07 Feb 2023Submission Checks Completed
07 Feb 2023Assigned to Editor
19 Feb 2023Review(s) Completed, Editorial Evaluation Pending
21 Feb 2023Reviewer(s) Assigned
03 Jul 2023Editorial Decision: Revise Major
17 Jul 20231st Revision Received
22 Jul 2023Submission Checks Completed
22 Jul 2023Assigned to Editor
22 Jul 2023Review(s) Completed, Editorial Evaluation Pending
22 Jul 2023Reviewer(s) Assigned
17 Sep 2023Editorial Decision: Accept