Global existence and exponential decay of solutions for generalized coupled non-degenerate Kirchhoff system with a time varying delay term

The paper studies a system of nonlinear viscoelastic Kirchhoff system with a time varying delay and general coupling terms. We prove the global existence of solutions in a bounded domain using the energy and Faedo–Galerkin methods with respect to the condition on the parameters in the coupling terms...

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Bibliographic Details
Published in:Boundary value problems 2020-05, Vol.2020 (1), p.1-28, Article 90
Main Authors: Mezouar, Nadia, Boulaaras, Salah
Format: Article
Language:English
Subjects:
Analysis
Approximations and Expansions
Coupling
Delay
Delay function
Difference and Functional Equations
Exponential decay
Faedo–Galerkin method
Galerkin method
Global existence
Lyapunov functional
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Viscoelastic term
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Summary:The paper studies a system of nonlinear viscoelastic Kirchhoff system with a time varying delay and general coupling terms. We prove the global existence of solutions in a bounded domain using the energy and Faedo–Galerkin methods with respect to the condition on the parameters in the coupling terms together with the weight condition as regards the delay terms in the feedback and the delay speed. Furthermore, we construct some convex function properties, and we prove the uniform stability estimate.
ISSN:1687-2770
1687-2762
1687-2770
DOI:10.1186/s13661-020-01390-9