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The Singular Perturbation Problem for a Class of Generalized Logistic Equations Under Non-classical Mixed Boundary Conditions

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Fernández-Rincón, Sergio and López-Gómez, Julián (2019) The Singular Perturbation Problem for a Class of Generalized Logistic Equations Under Non-classical Mixed Boundary Conditions. Advanced Nonlinear Studies, 19 (1). pp. 1-27. ISSN 1536-1365

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Abstract

This paper studies a singular perturbation result for a class of generalized diffusive logistic equa- tions, dLu = uh(u, x), under non-classical mixed boundary conditions, Bu = 0 on ∂Ω. Most of the precursors of this result dealt with Dirichlet boundary conditions and self-adjoint second order elliptic operators. To over- come the new technical difficulties originated by the generality of the new setting, we have characterized the regularity of ∂Ω through the regularity of the associated conormal projections and conormal distances. This seems to be a new result of a huge relevance on its own. It actually complements some classical findings of Serrin, Gilbarg and Trudinger, Krantz and Parks, Foote, and Li and Nirenberg concerning the regularity of the inner distance function to the boundary.


Item Type:Article
Uncontrolled Keywords:Perturbaciones singulares (Matemáticas)
Palabras clave (otros idiomas):Singular Perturbation, Positive Solution, Generalized Logistic Equation, Non-classical Mixed Boundary Conditions, Conormal Vector Field, Conormal Projection, Conormal Distance, Regularity
Subjects:Sciences > Mathematics
Sciences > Mathematics > Mathematical analysis
ID Code:54730
Deposited On:20 Mar 2019 10:30
Last Modified:20 Mar 2019 11:40

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