Heat Equation with Memory in Anisotropic and Non-Homogeneous Media

    Authors

    J. M. Yong;X. Zhang

    Comments

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    Abbreviated Journal Title

    Acta. Math. Sin.-English Ser.

    Keywords

    Heat equation with memory; anisotropic and non-homogeneous media; well-posedness; propagation speed; FINITE PROPAGATION SPEED; INTEGRODIFFERENTIAL EQUATIONS; EVOLUTION-EQUATIONS; WAVE-PROPAGATION; LA CHALEUR; CONDUCTION; DERIVATIVES; LEQUATION; THEOREM; Mathematics, Applied; Mathematics

    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.

    Journal Title

    Acta Mathematica Sinica-English Series

    Volume

    27

    Issue/Number

    2

    Publication Date

    1-1-2011

    Document Type

    Article

    Language

    English

    First Page

    219

    Last Page

    254

    WOS Identifier

    WOS:000286122700001

    ISSN

    1439-8516

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