Open AccessWell-Posedness and Stability for a System of Klein-Gordon Equations
Author(s) -
Naaima Latioui,
Amar Guesmia,
Amar Ouaoua
Publication year - 2022
Publication title -
international journal of analysis and applications
Language(s) - English
Resource type - Journals
ISSN - 2291-8639
DOI - 10.28924/2291-8639-20-2022-10
Subject(s) - uniqueness , mathematics , compact space , stability (learning theory) , lyapunov function , function (biology) , galerkin method , klein–gordon equation , mathematical analysis , pure mathematics , nonlinear system , computer science , physics , quantum mechanics , machine learning , evolutionary biology , biology
In this paper, we study the weak existence of solution for a non-linear hyperbolic coupled system of Klein-Gordon equations with memory and source terms using the Faedo-Galerkin method techniques and compactness results, we have demonstrated the uniqueness of the solution by using the classical technique. In addition, we show that the solution remains stable over time. The reaction of the proper Lyapunov function is the primary tool of the proof.