Convergence of a mass conserving Allen-Cahn equation whose Lagrange\n multiplier is nonlocal and local

2013/03/14 by Matthieu Alfaro, Alfaro, Matthieu, Pierre Alifrangis +1 · 2 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1303.3553

openalex publication_date 2013/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the mass conserving Allen-Cahn equation proposed in\n citeBra-Bre: the Lagrange multiplier which ensures the conservation of the\nmass contains not only nonlocal but also local effects (in contrast with\n citeChe-Hil-Log). As a parameter related to the thickness of a diffuse\ninternal layer tends to zero, we perform formal asymptotic expansions of the\nsolutions. Then, equipped with these approximate solutions, we rigorously prove\nthe convergence to the volume preserving mean curvature flow, under the\nassumption that classical solutions of the latter exist. This requires a\nprecise analysis of the error between the actual and the approximate Lagrange\nmultipliers.\n

Cited by

• Unconditionally stable exponential time differencing schemes for the mass-conserving Allen-Cahn equation with nonlocal and local effects
• Global solutions to the volume-preserving mean-curvature flow

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