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.
A mixed type identification problem related to a phase-field model with memory / D. Guidetti, A. Lorenzi. - In: OSAKA JOURNAL OF MATHEMATICS. - ISSN 0030-6126. - 44:3(2007), pp. 579-613.
A mixed type identification problem related to a phase-field model with memory
A. LorenziUltimo
2007
Abstract
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.Pubblicazioni consigliate
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