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Volume 37, Issue 4
Global Existence and Stability for a Viscoelastic Wave Equation with Nonlinear Boundary Source Term

Mohamed Mellah, Ali Hakem & Gongwei Liu

DOI: 10.4208/jpde.v37.n4.6

J. Part. Diff. Eq., 37 (2024), pp. 467-481.

Published online: 2024-12

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  • Abstract

This work considers the initial boundary value problem for a viscoelastic wave equation with a nonlinear boundary source term. Under suitable assumptions, we prove the existence of global weak solutions using the Galerkin approximation. Then, we give a decay rate estimate of the energy by making use of the perturbed energy method.

  • Keywords

Viscoelastic equation, nonlinear boundary source, stabilization.

  • AMS Subject Headings

35B44, 35D30, 35L30, 35L82

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-37-467, author = {Mellah , MohamedHakem , Ali and Liu , Gongwei}, title = {Global Existence and Stability for a Viscoelastic Wave Equation with Nonlinear Boundary Source Term}, journal = {Journal of Partial Differential Equations}, year = {2024}, volume = {37}, number = {4}, pages = {467--481}, abstract = {

This work considers the initial boundary value problem for a viscoelastic wave equation with a nonlinear boundary source term. Under suitable assumptions, we prove the existence of global weak solutions using the Galerkin approximation. Then, we give a decay rate estimate of the energy by making use of the perturbed energy method.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v37.n4.6}, url = {http://global-sci.org/intro/article_detail/jpde/23691.html} }
TY - JOUR T1 - Global Existence and Stability for a Viscoelastic Wave Equation with Nonlinear Boundary Source Term AU - Mellah , Mohamed AU - Hakem , Ali AU - Liu , Gongwei JO - Journal of Partial Differential Equations VL - 4 SP - 467 EP - 481 PY - 2024 DA - 2024/12 SN - 37 DO - http://doi.org/10.4208/jpde.v37.n4.6 UR - https://global-sci.org/intro/article_detail/jpde/23691.html KW - Viscoelastic equation, nonlinear boundary source, stabilization. AB -

This work considers the initial boundary value problem for a viscoelastic wave equation with a nonlinear boundary source term. Under suitable assumptions, we prove the existence of global weak solutions using the Galerkin approximation. Then, we give a decay rate estimate of the energy by making use of the perturbed energy method.

Mellah , MohamedHakem , Ali and Liu , Gongwei. (2024). Global Existence and Stability for a Viscoelastic Wave Equation with Nonlinear Boundary Source Term. Journal of Partial Differential Equations. 37 (4). 467-481. doi:10.4208/jpde.v37.n4.6
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