Title

Heat Equation With Memory In Anisotropic And Non-Homogeneous Media

Keywords

anisotropic and non-homogeneous media; Heat equation with memory; propagation speed; well-posedness

Abstract

A modified Fourier's law in an anisotropic and non-homogeneous media results in a heat equation with memory, for which the memory kernel is matrix-valued and spatially dependent. Different conditions on the memory kernel lead to the equation being either a parabolic type or a hyperbolic type. Well-posedness of such a heat equation is established under some general and reasonable conditions. It is shown that the propagation speed for heat pulses could be either infinite or finite, depending on the different types of the memory kernels. Our analysis indicates that, in the framework of linear theory, heat equation with hyperbolic kernel is a more realistic model for the heat conduction, which might be of some interest in physics. © 2011 Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg.

Publication Date

2-1-2011

Publication Title

Acta Mathematica Sinica, English Series

Volume

27

Issue

2

Number of Pages

219-254

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/s10114-010-0077-1

Socpus ID

78651443352 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/78651443352

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