Singular Perturbation Problem in Boundary/Fractional Combustion
Arshak Petrosyan, Wenhui Shi, Yannick Sire
TL;DR
This paper investigates a boundary-reaction-diffusion equation with combustion-type reactions related to the fractional Laplacian, establishing uniform regularity and analyzing the resulting free boundary problem.
Contribution
It introduces a novel approach to studying singular perturbations in fractional combustion problems, including regularity results and free boundary analysis.
Findings
Established optimal uniform Hölder regularity of solutions
Analyzed the limiting free boundary problem
Linked the problem to fractional Laplacian properties
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.