Stability of solutions for a heat equation with memory

Nasser Eddine Tatar, Sebti Kerbal, Asma Al-Ghassani

Research output: Contribution to journalArticle

Abstract

This article concerns the heat equation with a memory term in the form of a time-convolution of a kernel with the time-derivative of the state. This problem appears in oil recovery simulation in fractured rock reservoir. It models the fluid flow in a fissured media where the history of the flow must be taken into account. Most of the existing papers on related works treat only (in addition to the well-posedness which is by now well understood in various spaces) the convergence of solutions to the equilibrium state without establishing any decay rate. In the present work we shall improve and extend the existing results. In addition to weakening the conditions on the kernel leading to exponential decay, we extend the decay rate to a general one.

Original languageEnglish
Article number303
JournalElectronic Journal of Differential Equations
Volume2017
Publication statusPublished - Dec 11 2017

Keywords

  • Exponential stability
  • Fissure media
  • Fractured reservoir
  • Heat equation
  • Memory term

ASJC Scopus subject areas

  • Analysis

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