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Asymptotic Analysis· 2026Q1

Stability of a Degenerate Thermoelastic Equation

Kaïs Ammari, Fathi Hassine, Luc Robbiano

Short summary

A degenerate thermoelastic model for a rod shows uniform energy decay over time, proving well-posedness and stability for both weak and strong degeneracy cases.

AI-generated from the title and abstract; the full text is not read.

Key points

  • Analyzes a linear thermoelastic model of a rod with coupled heat and wave equations.
  • Investigates both weak and strong degeneracy at the x=0 endpoint.
  • Proves uniform energy decay for classical solutions using C0-semigroup theory and frequency domain methods.
  • Establishes well-posedness and asymptotic stability for the degenerate systems.

AI-generated from the title and abstract; the full text is not read.

Abstract

This work is dedicated to the study of a linear model arising in a thermoelastic rod of homogeneous material. The system results 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 endpoint 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 C 0 -semigroup theory and 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.

The authors' abstract, as published at the source. Asymptotic Analysis, 2026 · DOI ↗

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Field: Computational Theory and Mathematics

Computational Theory and MathematicsComputer Science