Osaka Journal of Mathematics

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

Davide Guidetti and Alfredo Lorenzi

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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.

Article information

Source
Osaka J. Math., Volume 44, Number 3 (2007), 579-613.

Dates
First available in Project Euclid: 13 September 2007

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1189717424

Mathematical Reviews number (MathSciNet)
MR2360942

Zentralblatt MATH identifier
1133.35106

Subjects
Primary: 35R30: Inverse problems 45K05: Integro-partial differential equations [See also 34K30, 35R09, 35R10, 47G20] 35M10: Equations of mixed type

Citation

Guidetti, Davide; Lorenzi, Alfredo. A mixed type identification problem related to a phase-field model with memory. Osaka J. Math. 44 (2007), no. 3, 579--613. https://projecteuclid.org/euclid.ojm/1189717424


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