Controllability and observability of a heat equation with hyperbolic memory kernel

    Authors

    X. Y. Fu; J. M. Yong;X. Zhang

    Comments

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    Abbreviated Journal Title

    J. Differ. Equ.

    Keywords

    Heat equation with memory; Controllability; Observability estimate; Carleman estimate; Highly concentrated approximate solution; INTEGRODIFFERENTIAL EQUATION; SYSTEMS; Mathematics

    Abstract

    The exact controllability and observability for a heat equation with hyperbolic memory kernel in anisotropic and nonhomogeneous media are considered. Due to the appearance of such a kind of memory, the speed of propagation for solutions to the heat equation is finite and the corresponding controllability property has a certain nature similar to hyperbolic equations, and is significantly different from that of the usual parabolic equations. By means of Carleman estimate, we establish a positive controllability and observability result under some geometric condition. On the other hand, by a careful construction of highly concentrated approximate solutions to hyperbolic equations with memory, we present a negative controllability and observability result when the geometric condition is not satisfied. (C) 2009 Elsevier Inc. All rights reserved.

    Journal Title

    Journal of Differential Equations

    Volume

    247

    Issue/Number

    8

    Publication Date

    1-1-2009

    Document Type

    Article

    Language

    English

    First Page

    2395

    Last Page

    2439

    WOS Identifier

    WOS:000270563900010

    ISSN

    0022-0396

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