Singular Perturbation Problem in Boundary/Fractional Combustion
Analysis of PDEs
2015-08-20 v1
Abstract
Motivated by a nonlocal free boundary problem, we study uniform properties of solutions to a singular perturbation problem for a boundary-reaction-diffusion equation, where the reaction term is of combustion type. This boundary problem is related to the fractional Laplacian. After an optimal uniform H\"older regularity is shown, we pass to the limit to study the free boundary problem it leads to.
Cite
@article{arxiv.1508.04583,
title = {Singular Perturbation Problem in Boundary/Fractional Combustion},
author = {Arshak Petrosyan and Wenhui Shi and Yannick Sire},
journal= {arXiv preprint arXiv:1508.04583},
year = {2015}
}