Nonlocal diffusion problems that approximate the heat equation with Dirichlet boundary conditions

被引：69

作者：

Cortazar, Carmen ^{[1
]}

Elgueta, Manuel ^{[1
]}

Rossi, Julio D. ^{[2
]}

机构：

[1] Catholic Univ Chile, Dept Matemat, Santiago 22, Chile

[2] Univ Buenos Aires, FCEyN, Dept Matemat, RA-1428 Buenos Aires, DF, Argentina

来源：

ISRAEL JOURNAL OF MATHEMATICS | 2009年 / 170卷 / 01期

关键词：

CAHN-HILLIARD EQUATION; PHASE-TRANSITIONS; CONVOLUTION MODEL; STABILITY;

D O I：

10.1007/s11856-009-0019-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We present a model for nonlocal diffusion with Dirichlet boundary conditions in a bounded smooth domain. We prove that solutions of properly rescaled nonlocal problems approximate uniformly the solution of the corresponding Dirichlet problem for the classical heat equation.

引用

页码：53 / 60

页数：8

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