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Vol. 52 No. 3 (2026)
Serdica Mathematical Journal

Articles

Asymptotic stability of singular solutions for the hyperelastic rod equation

https://doi.org/10.55630/serdica.2026.52.295-312

Published 25-09-2026

  • Mehmed Kodzha

Mehmed Kodzha
Shumen University

Abstract

We consider a hyperelastic rod equation that includes the integrable Camassa-Holm equation. We construct singular wave solutions and study their asymptotic stability near the blow-up time. To this end, we introduce suitable transformations and reformulate the problem as a dissipative quasilinear evolution equation. By employing rigorous energy estimates, commutator bounds, and semigroup theory, we demonstrate how the stability properties strongly depend on the parameter ranges of the equation.

2020 Mathematics Subject Classification:

35B40, 35B35, 35Q99

Keywords

rod equation, singular solutions, asymptotic stability

Full text

Author Details

Mehmed Kodzha

Faculty of Mathematics and Informatics
Shumen University
Shumen, Bulgaria
e-mail: mkodzha@gmail.com

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