Work

General Decay and Blowing‐Up Solutions of a Nonlinear Wave Equation With Nonlocal in Time Damping and Infinite Memory

Year: 2025

Type: article

Abstract: 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.

Source: Mathematical Methods in the Applied Sciences

DOI: 10.1002/mma.10777

Authors: Mokhtar Kirane, Radhouane Aounallah, Lotfi Jlali

Institutions: Khalifa University of Science and Technology, Université Djilali de Sidi Bel Abbès, Imam Mohammad ibn Saud Islamic University

Language: English

Topic: Stability and Controllability of Differential Equations

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $5,000

Funder: Al-Imam Muhammad Ibn Saud Islamic University