Stability of solutions for a heat equation with memory
Date
2017-12-11
Authors
Tatar, Nasser Eddine
Kerbal, Sebti
Al-Ghassani, Asma
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
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.
Description
Keywords
Heat equation, Memory term, Exponential stability, Fractured reservoir, Fissure media
Citation
Tatar, N. E., Kerbal, S., & Al-Ghassani, A. (2017). Stability of solutions for a heat equation with memory. <i>Electronic Journal of Differential Equations, 2017</i>(303), pp. 1-16.
Rights
Attribution 4.0 International