2024/10/09 by Kaïs Ammari, Ammari, Kaïs, Fathi Hassine +3
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Numerical methods in inverse problems #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.2410.06732
openalex publication_date 2024/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This work is dedicated to the study of a linear model arising in thermoelastic rod of homogeneous material. The system is resulting from a coupling of a heat and a wave equation in the interval (0,1) with Dirichlet boundary conditions at the outer endpoints where the parabolic component is degenerating at the end point x=0. Two models are considered the first is with weak degeneracy and the second is with strong degeneracy. We aim to study the well-posedness and asymptotic stability of both systems using techniques from the C0-semigroup theory and a use a frequency domain approach based on the well-known result of Prüss in order to prove using some multiplier techniques that the energy of classical solutions decays uniformly as time goes to infinity.