The Singular Perturbation Problem for a Class of Generalized Logistic Equations Under Non-classical Mixed Boundary Conditions
This paper studies a singular perturbation result for a class of generalized diffusive logistic equations, dℒu=uh(u,x){d\mathcal{L}u=uh(u,x)}, under non-classical mixed boundary conditions, ℬu=0{\mathcal{B}u=0} on ∂Ω{\partial\Omega}. Most of the precursors of this result dealt with Dirichlet b...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2019-02-01
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| Series: | Advanced Nonlinear Studies |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/ans-2018-2034 |
| Summary: | This paper studies a singular perturbation result for a class of generalized diffusive logistic equations, dℒu=uh(u,x){d\mathcal{L}u=uh(u,x)}, under non-classical mixed boundary conditions, ℬu=0{\mathcal{B}u=0} on ∂Ω{\partial\Omega}. Most of the precursors of this result dealt with Dirichlet boundary conditions and self-adjoint second order elliptic operators. To overcome the new technical difficulties originated by the generality of the new setting, we have characterized the regularity of ∂Ω{\partial\Omega} 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, [39], Gilbarg and Trudinger, [21], Krantz and Parks, [27], Foote, [18] and Li and Nirenberg [28] concerning the regularity of the inner distance function to the boundary. |
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| ISSN: | 1536-1365 2169-0375 |