Existence and Blow-up Study of a Quasilinear Wave Equation with Damping and Source Terms of Variable Exponents-type Acting on the Boundary

In this work, we are concerned with a quasilinear wave equation with nonlinear damping and source terms of variable exponents-type acting in a part of the boundary. Under suitable conditions on the exponents and the initial data, we study the blow-up properties. Firstly, by using Faedo-Galerkin meth...

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Bibliographic Details
Published in:Journal of dynamical and control systems 2024-06, Vol.30 (2), Article 11
Main Authors: Kafini, Mohammad, Al-Gharabli, Mohammad M., Al-Mahdi, Adel M.
Format: Article
Language:English
Subjects:
Calculus of Variations and Optimal Control
Optimization
Control
Damping
Dynamical Systems
Dynamical Systems and Ergodic Theory
Existence theorems
Exponents
Fixed points (mathematics)
Galerkin method
Mathematics
Mathematics and Statistics
Systems Theory
Upper bounds
Vibration
Wave equations
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Summary:In this work, we are concerned with a quasilinear wave equation with nonlinear damping and source terms of variable exponents-type acting in a part of the boundary. Under suitable conditions on the exponents and the initial data, we study the blow-up properties. Firstly, by using Faedo-Galerkin method and Banach-Fixed-Point Theorem, we establish the existence of a weak solution, under suitable assumptions on the variable exponents and the initial data. Secondly, we show a finite time blow-up with lower and upper bound as well. Next, an infinite time blow-up is proved under some conditions in the exponents and the initial data.
ISSN:1079-2724
1573-8698
DOI:10.1007/s10883-024-09695-z