Singular perturbation problem in boundary/fractional combustion

被引：2

作者：

Petrosyan, Arshak ^{[1
]}

Shi, Wenhui ^{[2
]}

Sire, Yannick ^{[3
]}

机构：

[1] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

[2] Univ Bonn, Math Inst, Endenicher Allee 62, D-53115 Bonn, Germany

[3] Univ Aix Marseille, Inst Math Marseille, CMI, Technopole Chateau Gombert, Marseille, France

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2016年 / 138卷

关键词：

Fractional/boundary reaction-diffusion problem; Singular perturbation problem; Uniform estimates; FREE-BOUNDARY PROBLEM; ELLIPTIC-EQUATIONS; REGULARITY; LIMIT;

D O I：

10.1016/j.na.2015.12.019

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 Holder regularity is shown, we pass to the limit to study the free boundary problem it leads to. (C) 2015 Elsevier Ltd. All rights reserved.

引用

页码：346 / 368

页数：23

共 50 条

[41] A Schrodinger singular perturbation problem
Ramm, A. G.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2007, 12 (08) : 1390 - 1394
[42] A SINGULAR PROBLEM OF PERTURBATION THEORY
MOSER, J
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1954, 60 (04) : 342 - 342
[43] A singular perturbation problem in magnetohydrodynamics
Cimatti, Giovanni
IMA JOURNAL OF APPLIED MATHEMATICS, 2010, 75 (02) : 240 - 245
[44] A nonlinear singular perturbation problem
Mathematics Department, Kansas State University, Manhattan, KS 66506-2602, United States
Asymptotic Anal, 2006, 1-2 (49-54):
[45] SINGULAR PERTURBATION OF FIRST BOUNDARY VALUE PROBLEM FOR HIGHER ORDER ELLIPTIC EQUATIONS(Ⅱ)
郑永树
Applied Mathematics and Mechanics(English Edition), 1981, (05) : 613 - 623
[46] SHOOTING METHOD IN SINGULAR PERTURBATION PROBLEM OF ORDINARY DIFFERENTIAL EQUATIONS WITH BOUNDARY LAYERS
凌复华
李继跃
AppliedMathematicsandMechanics(EnglishEdition), 1988, (07) : 659 - 665
[47] SINGULAR PERTURBATION OF GENERAL BOUNDARY VALUE PROBLEM FOR NONLINEAR DIFFERENTIAL EQUATION SYSTEM
周雅丽
游哲丰
林宗池
AppliedMathematicsandMechanics(EnglishEdition), 1998, (06) : 531 - 538
[48] NONLINEAR SINGULAR PERTURBATION BOUNDARY-VALUE PROBLEM IN GAS LUBRICATION THEORY
STEINMETZ, WJ
SIAM JOURNAL ON APPLIED MATHEMATICS, 1974, 26 (04) : 816 - 827
[49] Singular perturbation of general boundary value problem for nonlinear differential equation system
Zhou, YL
You, ZF
Lin, ZC
APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION, 1998, 19 (06) : 531 - 538
[50] ON NUMERICAL-SOLUTION OF A SINGULAR PERTURBATION PROBLEM WITH MIXED BOUNDARY-CONDITIONS
VULANOVIC, R
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 1986, 66 (05): : T334 - T335

← 1 2 3 4 5 →