CONVERGENCE OF A ONE-DIMENSIONAL CAHN-HILLIARD EQUATION WITH DEGENERATE MOBILITY

被引:3
作者
Delgadino, Matias G. [1 ]
机构
[1] Univ Maryland, Dept Math, College Pk, MD 20742 USA
关键词
gradient flow; Cahn-Hilliard; Wasserstein; gamma convergence; fourth-order parabolic equations; thin-film equation; GAMMA-CONVERGENCE; GRADIENT FLOWS; LUBRICATION APPROXIMATION; BIOLOGICAL AGGREGATION; SPACES; MODEL;
D O I
10.1137/15M1045429
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We consider a one-dimensional periodic forward-backward parabolic equation, regularized by a degenerate nonlinear fourth-order term of order epsilon(2) << 1. This equation is known in the literature as Cahn-Hilliard equation with degenerate mobility. Under the hypothesis of the initial data being well prepared, we prove that as epsilon -> 0, the solution converges to the solution of a wellposed degenerate parabolic equation. The proof exploits the gradient flow nature of the equation in W-2(T) and utilizes the framework of convergence of gradient flows developed by Sandier and Serfaty (Comm. Pure Appl. Math., 57 (2004), pp. 1627-1672; Discrete Contin. Dyn. Syst., 31 (2011), pp. 1427-1451). As an incidental, we study fine energetic properties of solutions to the thin-film equation partial derivative(t)v = -(vv(xxx))(x).
引用
收藏
页码:4457 / 4482
页数:26
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