Singular perturbation problem in boundary/fractional combustion to our friend Juan-Luis Vázquez for his 70th birthday

Arshak Petrosyan, Wenhui Shi, Yannick Sire

Research output: Contribution to journalArticleResearchpeer-review

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.

Original languageEnglish
Pages (from-to)346-368
Number of pages23
JournalNonlinear Analysis, Theory, Methods and Applications
Volume138
DOIs
Publication statusPublished - 1 Jun 2016
Externally publishedYes

Keywords

  • Fractional/boundary reaction-diffusion problem
  • Singular perturbation problem
  • Uniform estimates

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