Differential and Integral Equations

On a Penrose-Fife phase-field model with nonhomogeneous Neumann boundary conditions for the temperature

Pierluigi Colli, Gianni Gilardi, Elisabetta Rocca, and Giulio Schimperna

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This work is concerned with the study of an initial and boundary value problem for a nonconserved system of phase field equations arising from the Penrose-Fife approach to phase transitions problems. Several works deal with variations of the same problem coupled with third type boundary conditions for the heat flux. On the contrary, our aim is to consider the case of the nonhomogeneous Neumann boundary condition for the heat flux, to find well-posedness for a weak formulation of this problem, and to prove a regularity result in case of smoother data and a slightly less general heat flux law.

Article information

Differential Integral Equations, Volume 17, Number 5-6 (2004), 511-534.

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K60: Nonlinear initial value problems for linear parabolic equations
Secondary: 35B45: A priori estimates 35D05 80A22: Stefan problems, phase changes, etc. [See also 74Nxx]


Colli, Pierluigi; Gilardi, Gianni; Rocca, Elisabetta; Schimperna, Giulio. On a Penrose-Fife phase-field model with nonhomogeneous Neumann boundary conditions for the temperature. Differential Integral Equations 17 (2004), no. 5-6, 511--534. https://projecteuclid.org/euclid.die/1356060345

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