A fourth order wave equation with acoustic boundary conditions: asymptotic behavior and blow-up in finite time

Abstract This work is devoted to the study of an initial boundary value problem for a fourth order wave equation with weak damping, source term, and acoustic boundary conditions. Under suitable assumptions on the initial data, we prove the global existence, exponential decay and blow up of solutions with negative initial energy.

Authors

Zayd Hajjej (ORCID: https://orcid.org/0000-0003-0622-0779)
Nouri Boumaza (ORCID: https://orcid.org/0000-0001-5775-7766)
A. Imad (ORCID: https://orcid.org/0000-0002-3174-987X)
Billel Gheraibia (ORCID: https://orcid.org/0000-0002-9473-603X)
Hongwei Zhang (ORCID: https://orcid.org/0000-0002-0898-7765)

Publication Details

Journal: Boundary Value Problems
Published: 2025-10-31
DOI: https://doi.org/10.1186/s13661-025-02142-3
Primary Topic: Stability and Controllability of Differential Equations
Type: article
Field-Weighted Citation Impact: 0.00

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article

A fourth order wave equation with acoustic boundary conditions: asymptotic behavior and blow-up in finite time

Zayd Hajjej, Nouri Boumaza, A. Imad, Billel Gheraibia et al.

Oct 31, 2025

Boundary Value Problems

Stability and Controllability of Differential Equations

article

A fourth order wave equation with acoustic boundary conditions: asymptotic behavior and blow-up in finite time

Zayd Hajjej, Nouri Boumaza, A. Imad, Billel Gheraibia, Hongwei Zhang

October 31, 2025article en

Abstract

Abstract This work is devoted to the study of an initial boundary value problem for a fourth order wave equation with weak damping, source term, and acoustic boundary conditions. Under suitable assumptions on the initial data, we prove the global existence, exponential decay and blow up of solutions with negative initial energy.

Boundary Value ProblemsVol. 2025(1)

Openalex Percentile: Top 60%

Stability and Controllability of Differential Equations

DOI Open Access PDF OpenAlex

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