Well-posedness and stability for a viscoelastic Petrovsky equation with a localized nonlinear damping

• Zineb Sabbagh ^[1] ; Ammar Khemmoudj ^[2] ; Mama Abdelli ^[3]
  1. [1] Faculty of Sciences, M’hamed Bougara University, Boumerdes, Algeria
  2. [2] Laboratory of SD, Faculty of Mathematics, University of Science and Technology Houari Boumediene, Algeria
  3. [3] Laboratory of Analysis and Control of Partial Differential Equations, Djillali Liabes University, Algeria

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• Localización: SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada, ISSN-e 2254-3902, ISSN 2254-3902, Vol. 81, Nº. 2, 2024, págs. 307-328
• Idioma: inglés
• DOI: 10.1007/s40324-023-00325-5
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• Resumen

  • In this paper, we consider a viscoelastic Petrovsky equation with localised nonlinear damping in bounded domain. The nonlinear damping is effective only in a neighborhood of a suitable subset of the boundary. Using the Faedo–Galerkin approximations together with some energy estimates, we prove the global existence of the solutions. Under the same assumptions, exponential decay results of the energy are established via suitable Lyapunov functionals.