On the global existence, exponential decay and blow-up of a nonlinear wave equation subject to a boundary fractional damping and time-varying delay
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- 1 January 2026
- journal article
- Published by American Institute of Mathematical Sciences (AIMS) in Discrete and Continuous Dynamical Systems - S
- Vol. 23, 178-196
Abstract
This study examines a nonlinear wave equation with boundary fractional damping and time-varying delay. After proving the existence of a global solution, we establish exponential stability by constructing an appropriate Lyapunov functional. Finally, we prove the blow-up phenomenon using the potential-well method.Keywords
This publication has 27 references indexed in Scilit:
- Global existence and general decay of solutions for a wave equation with memory, fractional boundary damping terms and logarithmic non-linearityPartial Differential Equations in Applied Mathematics, 2024
- Local existence, global existence and decay results of a logarithmic wave equation with delay termMathematical Methods in the Applied Sciences, 2022
- General decay of nonlinear viscoelastic Kirchhoff equation with Balakrishnan‐Taylor damping, logarithmic nonlinearity and distributed delay termsMathematical Methods in the Applied Sciences, 2020
- Blow-up and asymptotic behavior for a wave equation with a time delay condition of fractional typeRendiconti del Circolo Matematico di Palermo Series 2, 2020
- General decay and blow up of solution for a nonlinear wave equation with a fractional boundary dampingMathematical Methods in the Applied Sciences, 2020
- The Euler–Bernoulli beam equation with boundary dissipation of fractional derivative typeMathematical Methods in the Applied Sciences, 2016
- Blow up of positive initial energy solutions for a wave equation with fractional boundary dissipationApplied Mathematics Letters, 2011
- Fractional Dynamics2010
- Existence and nonexistence of global solutions of some system of semilinear wave equationsNonlinear Analysis, 2003
- On potential wells and vacuum isolating of solutions for semilinear wave equationsJournal of Differential Equations, 2003