Singular perturbation problem in boundary/fractional combustion

Arshak Petrosyan (1) , Wenhui Shi (2) , Yannick Sire (3)

1 Department of mathematics Purdue University
2 HCM - Hausdorff Center for Mathematics
3 I2M - Institut de Mathématiques de Marseille

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.

Mots clés: fractional/boundary reaction-diffusion problem; singular perturbation problem; uniform estimates

Domaines: Equations aux dérivées partielles [math.AP]

Arshak Petrosyan, Wenhui Shi, Yannick Sire. Singular perturbation problem in boundary/fractional combustion. Nonlinear Analysis: Theory, Methods and Applications, 2016, 138, pp.346--368. ⟨10.1016/j.na.2015.12.019⟩. ⟨hal-01338448⟩