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WELL-POSEDNESS AND GENERAL ENERGY DECAY OF SOLUTION FOR TRANSMISSION PROBLEM WITH WEAKLY NONLINEAR DISSIPATIVE
Journal article   Peer reviewed

WELL-POSEDNESS AND GENERAL ENERGY DECAY OF SOLUTION FOR TRANSMISSION PROBLEM WITH WEAKLY NONLINEAR DISSIPATIVE

Noureddine Bahri, Mama Abdelli, Abderrahmane Beniani and Khaled Zennir
The Journal of integral equations and applications, Vol.33(2), pp.155-170
01/06/2021
DOI: https://doi.org/10.1216/jie.2021.33.155

Abstract

Mathematics Mathematics, Applied Physical Sciences Science & Technology
In this paper, we consider a transmission problem in a bounded domain with a nonlinear dissipation in the first equation. Under suitable assumptions on the weight of the damping, we show the existence and uniqueness of solution by the Faedo-Galerkin method. Also we prove general stability estimates using some properties of convex functions and Lyaponov functional.

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