Electronic Journal of Differential Equations,
Vol. 2006(2006), No. 152, pp. 1-10.

Title: Truncated gradient flows of the van der Waals free energy

Authors: Michael Grinfeld (Univ. of Strathclyde, Scotland, UK)
         Iulian Stoleriu ("Al. I. Cuza", Univ., Iasi, Romania)
	 
Abstract: 
 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.