Relaxation of the flow of triods by curve shortening flow via the vector-valued parabolic Allen-Cahn equation

DOI10.1515/CRELLE.2009.071zbMath1188.53074arXiv0706.3299MaRDI QIDQ3645145

Mariel Sáez Trumper

Publication date: 16 November 2009

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0706.3299

zbMATH Keywords

curve shortening flowvector-valued parabolic Allen-Cahn equation

Mathematics Subject Classification ID

Related Items (4)

Convergence of the scalar- and vector-valued Allen–Cahn equation to mean curvature flow with 90°-contact angle in higher dimensions, part I: Convergence result ⋮ Some new computational methods for the Allen‐Cahn equation with non‐periodic boundary conditions arising in computational fluid dynamics ⋮ Entire solutions to equivariant elliptic systems with variational structure ⋮ Uniqueness of Self-Similar Solutions to the Network Flow in a Given Topological Class

Cites Work

• Analysis of the heteroclinic connection in a singularly perturbed system arising from the study of crystalline grain boundaries
• Generation and propagation of interfaces for reaction-diffusion equations
• On three-phase boundary motion and the singular limit of a vector-valued Ginzburg-Landau equation
• Stationary layered solutions in \(\mathbb{R}^ 2\) for an Allen-Cahn system with multiple well potential
• Phase transitions and generalized motion by mean curvature
• Front Propagation and Phase Field Theory
• A three-layered minimizer in R2 for a variational problem with a symmetric three-well potential
• Explicit stationary solutions in multiple well dynamics and non-uniqueness of interfacial energy densities

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