Structural identification of an unknown source term in a heat equation

    Authors

    J. R. Cannon;P. DuChateau

    Comments

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    Abbreviated Journal Title

    Inverse Probl.

    Keywords

    DIFFUSION EQUATION; INVERSE PROBLEM; Mathematics, Applied; Physics, Mathematical

    Abstract

    The identification of an unknown state-dependent source term in a reaction-diffusion equation is considered. Integral identities are derived which relate changes in the source term to corresponding changes in the measured output. The identities are used to show that the measured boundary output determines the source term uniquely in an appropriate function class and to show that a source term that minimizes an output least squares functional based on this measured output must also solve the inverse problem. The set of outputs generated by polygonal source functions is shown to be dense in the set of all admissible outputs. Results from some numerical experiments are discussed.

    Journal Title

    Inverse Problems

    Volume

    14

    Issue/Number

    3

    Publication Date

    1-1-1998

    Document Type

    Article

    Language

    English

    First Page

    535

    Last Page

    551

    WOS Identifier

    WOS:000074497500010

    ISSN

    0266-5611

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