Portugaliae Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
MATHEMATICA
Vol. 58, No. 2, pp. 159-170 (2001)

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Global Existence for The Conserved Phase Field Model with Memory and Quadratic Nonlinearity

P. Colli, G. Gilardi, M. Grasselli and G. Schimperna

Dipartimento di Matematica, Università di Pavia,
Via Ferrata 1, 27100 Pavia -- ITALY
E-mail: pier@dragon.ian.pv.cnr.it
Dipartimento di Matematica, Università di Pavia,
Via Ferrata 1, 27100 Pavia -- ITALY
E-mail: gilardi@dimat.unipv.it
Dipartimento di Matematica, Politecnico di Milano,
Via Bonardi 9, 20133 Milano -- ITALY
E-mail: maugra@mate.polimi.it
Dipartimento di Matematica, Università di Pavia,
Via Ferrata 1, 27100 Pavia -- ITALY
E-mail: schimper@dragon.ian.pv.cnr.it

Abstract: A nonlinear system for the heat diffusion inside a material subject to phase changes is considered. A thermal memory effect is assumed in the heat conduction law; moreover, on account of thermodynamical considerations, a linear growth is allowed for the latent heat density. The resulting problem couples a second order integrodifferential equation, derived from the balance of energy, with a fourth order parabolic inclusion which rules the evolution of an order parameter $\chi$. Homogeneous Neumann boundary conditions guarantee that the space average of $\chi$ is conserved in time. Global existence of solutions is proved in a variational setting.

Keywords: Conserved phase-field model; Integrodifferential evolution system; Heat transfer with memory; Maximal monotone graph; Bootstrap argument.

Classification (MSC2000): 35R99, 45K05, 80A22.

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Electronic version published on: 9 Feb 2006. This page was last modified: 27 Nov 2007.

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