Global existence and general decay estimates of solutions for a nonlinear system of coupled hyperbolic and parabolic equations

Mama Abdelli; Baowei Feng; Abbes Benaissa; Zayd Hajjej; Sabeur Mansouri

doi:10.4171/zaa/1813

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Global existence and general decay estimates of solutions for a nonlinear system of coupled hyperbolic and parabolic equations

Mama Abdelli
Djillali Liabes University, Sidi Bel Abbes, Algeria; University of Monastir, Tunisia
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Baowei Feng
Southwestern University of Finance and Economics, Chengdu, P. R. China
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Abbes Benaissa
Djillali Liabes University, Sidi Bel Abbes, Algeria
Zayd Hajjej
King Saud University, Riyadh, Saudi Arabia
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Sabeur Mansouri
University of Monastir, Tunisia
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Abstract

This paper is devoted to the study of a nonlinear system of coupled hyperbolic and parabolic equations. Initially, we establish the well-posedness of our system through the Faedo–Galerkin approach and derive its exponential stability by constructing a suitable Lyapunov functional in the non-degenerate case. Subsequently, we address the general stability in the degenerate case using integral inequalities.

Cite this article

Mama Abdelli, Baowei Feng, Abbes Benaissa, Zayd Hajjej, Sabeur Mansouri, Global existence and general decay estimates of solutions for a nonlinear system of coupled hyperbolic and parabolic equations. Z. Anal. Anwend. (2026), published online first

DOI 10.4171/ZAA/1813