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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

  • Baowei Feng

    Southwestern University of Finance and Economics, Chengdu, P. R. China

  • Abbes Benaissa

    Djillali Liabes University, Sidi Bel Abbes, Algeria

  • Zayd Hajjej

    King Saud University, Riyadh, Saudi Arabia

  • Sabeur Mansouri

    University of Monastir, Tunisia
Global existence and general decay estimates of solutions for a nonlinear system of coupled hyperbolic and parabolic equations cover

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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