Work

A convergence result for the derivation of front propagation in nonlocal phase field models

Year: 2024

Type: article

Abstract: We prove that the mean curvature of a smooth surface in \R^{n} , n\geq 2 , arises as the limit of a sequence of functions that are intrinsically related to the difference between an n - and 1 -dimensional fractional Laplacian of a phase transition. Depending on the order of the fractional Laplace operator, we recover the fractional mean curvature or the classical mean curvature of the surface. Moreover, we show that this is an essential ingredient for deriving the evolution of fronts in fractional reaction-diffusion equations such as those for atomic dislocations in crystals.

Source: Interfaces and Free Boundaries Mathematical Analysis Computation and Applications

DOI: 10.4171/ifb/531

Authors: Stefania Patrizi, Mary Vaughan

Institutions: The University of Texas at Austin, The University of Western Australia

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: National Science Foundation

Award: Nonlinear Partial Differential Equations Methods in the Study of Interfaces