Existence, uniqueness and stability of solutions for some parabolic-hyperbolic systèms with a neutral delay
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Date
2025
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Université Badji Mokhtar Annaba
Abstract
In this thesis, we are interested in the study of some systems of partial derivative equations. Using the theory of semigroups and the Faedo-Galerkin method, we establish the existence and uniqueness results of the solutions of some thermos-elastic systems of porous types via Lord Shulman's law with a neutral delay.
Afterwards, an exponential, polynomial and general stability results of the solution were proven based on the multipliers technique which consists to construct a Lyapunov functional equivalent to the energy of the systems studied.
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Keywords
polynomial stability; Faedo-Galerkin method; porous-elastic system