Geodesic
Well-Posedness and Asymptotic Stability of a Non-Linear Porous System with a Delay Term
Kragujevac Journal of Mathematics, Tome 48 (2024) no. 4, p. 591 .

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Our interest in this work is to treat a one-dimensional Porous system with a non-linear damping and a delay in the non-linear internal feedback. We prove the global existence and uniqueness of its solution in suitable function spaces by means of the Faedo-Galerkin procedure combined with the energy method under a suitable relation between the weight of the delayed feedback and the weight of the non-delayed feedback. Also, we give an explicit and general decay rate estimate by applying the well-known multiplier method integrated with some properties of convex functions and for two opposites cases with respect to the speeds of wave propagation.
DOI : 10.46793/KgJMat2404.591M
Classification : 35A02, 35D35, 35B40
Keywords: Non-linear Porous system, global existence, delay term, general decay, Faedo-Glaerkin method, multiplier method 
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Hocine Makheloufi; Nadia Mezouar; Mounir Bahlil. Well-Posedness and Asymptotic Stability of a Non-Linear Porous System with a Delay Term. Kragujevac Journal of Mathematics, Tome 48 (2024) no. 4, p. 591 . doi : 10.46793/KgJMat2404.591M. http://geodesic.mathdoc.fr/articles/10.46793/KgJMat2404.591M/

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