Solvability for phase field systems of Penrose-Fife type associated with $p$-laplacian diffusions

Pages: 927 - 937, Issue Special, September 2007

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Ken Shirakawa - Department of Applied Mathematics, Faculty of Engineering, Kobe University, 1-1 Rokkodai, Nada, Kobe, 657-8501, Japan (email)

Abstract: In this paper, we deal with systems of nonlinear evolution equations, which are mathematical models of phase transitions, classified as "Penrose-Fife type". In the presented models, $p$-Laplacians, with 1 $<= p$ < 2, are adopted to describe the diffusions in exchanges. As the main conclusions, some theorems, concerned with the existence and the uniqueness of solutions of our systems, will be proved, under appropriate assumptions.

Keywords:  Phase field systems, Penrose-Fife type, p-Laplacian diffusions.
Mathematics Subject Classification:  Primary: 35K55; Secondary: 82B26.

Received: September 2006;      Revised: February 2007;      Published: September 2007.