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September 2007 A mixed type identification problem related to a phase-field model with memory
Davide Guidetti, Alfredo Lorenzi
Osaka J. Math. 44(3): 579-613 (September 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.

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Davide Guidetti. Alfredo Lorenzi. "A mixed type identification problem related to a phase-field model with memory." Osaka J. Math. 44 (3) 579 - 613, September 2007.

Information

Published: September 2007
First available in Project Euclid: 13 September 2007

zbMATH: 1133.35106
MathSciNet: MR2360942

Subjects:
Primary: 35M10, 35R30, 45K05

Rights: Copyright © 2007 Osaka University and Osaka City University, Departments of Mathematics

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Vol.44 • No. 3 • September 2007
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