Electron. J. Diff. Eqns., Vol. 2006(2006), No. 152, pp. 1-9.

Truncated gradient flows of the van der Waals free energy

Michael Grinfeld, Iulian Stoleriu

We employ the Pade approximation to derive a set of new partial differential equations, which can be put forward as possible models for phase transitions in solids. We start from a nonlocal free energy functional, we expand in Taylor series the interface part of this energy, and then consider gradient flows for truncations of the resulting expression. We shall discuss here issues related to the existence and uniqueness of solutions of the newly obtained equations, as well as the convergence of the solutions of these equations to the solution of a nonlocal version of the Allen-Cahn equation.

Submitted November 1, 2006. Published December 5, 2006.
Math Subject Classifications: 47H20, 45J05, 35K55, 41A21.
Key Words: Gradient flow; van der Waals energy; integro-differential equation; Pade approximants.

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  Michael Grinfeld
Department of Mathematics, University of Strathclyde
26 Richmond Street, G1 1XH Glasgow
Scotland, United Kingdom
email: m.grinfeld@strath.ac.uk
Iulian Stoleriu
Faculty of Mathematics, "Al. I. Cuza" University
Bvd. Carol I, No. 11, 700506 Iasi, Romania.
EML Research gGmbH, Schloss Wolfsbrunnenweg 33
69118 Heidelberg, Germany
email: iulian.stoleriu@uaic.ro, iulian.stoleriu@eml-r.villa-bosch.de

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