General Decay and Blowing‐Up Solutions of a Nonlinear Wave Equation With Nonlocal in Time Damping and Infinite Memory
ABSTRACT This paper shows that long‐term stability and blowing‐up solutions for a nonlinear wave equation with a nonlocal damping of Choi and MacCamy type and a nonlocal dispersion can occur. The method of proof of general decay relies on a suitable Lyapunov functional. The method of proof of blow up in finite time of some solutions relies on the concavity method.
Authors
- Lotfi Jlali (ORCID: https://orcid.org/0000-0001-7604-0955)
- Radhouane Aounallah
- Mokhtar Kirane (ORCID: https://orcid.org/0000-0002-4867-7542)
Institutions
- Khalifa University of Science and Technology (AE)
- Imam Mohammad ibn Saud Islamic University (SA)
- Université Djilali de Sidi Bel Abbès (DZ)
Publication Details
- Journal
- Mathematical Methods in the Applied Sciences
- Published
- 2025-02-15
- DOI
- https://doi.org/10.1002/mma.10777
- Citations
- 8
- Primary Topic
- Advanced Mathematical Physics Problems
- Type
- article
- Field-Weighted Citation Impact
- 29.54
Funders
- Al-Imam Muhammad Ibn Saud Islamic University