A mixed type identification problem related to a phase-field model with memory

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In this paper we consider an integro-differential system consisting of a parabolic and a hyperbolic equation related to phase transition models. The first equation is integro-differential and of hyperbolic type. It describes the evolution of the temperature and also accounts for memory effects through a memory kernel k via the Gurtin-Pipkin heat flux law. The latter equation, governing the evolution of the order parameter, is semilinear, parabolic and of the fourth order (in space). We prove a local in time existence result and a global uniqueness result for the identification problem consisting in recovering the memory kernel k appearing in the first equation.

Journal

  • Osaka Journal of Mathematics

    Osaka Journal of Mathematics 44 (3), 579-613, 2007-09

    Osaka University and Osaka City University, Departments of Mathematics

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