Identifying a space dependent coefficient in a reaction-diffusion equation

Elena Beretta, Cecilia Cavaterra

    Research output: Contribution to journalArticle

    Abstract

    We consider a reaction-difiusion equation for the front motion u in which the reaction term is given by c(x)g(u). We formulate a suitable inverse problem for the unknowns u and c, where u satisfies homogeneous Neumann boundary conditions and the additional condition is of integral type on the time interval [0; T]. Uniqueness of the solution is proved in the case of a linear g. Assuming g non linear, we show uniqueness for large T.

    Original languageEnglish (US)
    Pages (from-to)285-296
    Number of pages12
    JournalInverse Problems and Imaging
    Volume5
    Issue number2
    DOIs
    StatePublished - May 1 2011

    Fingerprint

    Reaction-diffusion Equations
    Inverse problems
    Uniqueness
    Boundary conditions
    Dependent
    Coefficient
    Neumann Boundary Conditions
    Inverse Problem
    Unknown
    Interval
    Motion
    Term

    Keywords

    • Inverse problems
    • Reaction-difiusion equations

    ASJC Scopus subject areas

    • Analysis
    • Modeling and Simulation
    • Discrete Mathematics and Combinatorics
    • Control and Optimization

    Cite this

    Identifying a space dependent coefficient in a reaction-diffusion equation. / Beretta, Elena; Cavaterra, Cecilia.

    In: Inverse Problems and Imaging, Vol. 5, No. 2, 01.05.2011, p. 285-296.

    Research output: Contribution to journalArticle

    Beretta, Elena ; Cavaterra, Cecilia. / Identifying a space dependent coefficient in a reaction-diffusion equation. In: Inverse Problems and Imaging. 2011 ; Vol. 5, No. 2. pp. 285-296.
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