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Continuity of the dynamics in a localized large diffusion problem with nonlinear boundary conditions |
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| Authors: | Vera Lú cia Carbone,Karina Schiabel-Silva |
| Affiliation: | a Departamento de Matemática, Universidade Federal de São Carlos, Caixa Postal 676, 13.565-905 São Carlos SP, Brazil b Departamento de Matemática, Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo-Campus de São Carlos, Caixa Postal 668, 13560-970 São Carlos SP, Brazil |
| Abstract: | This paper is concerned with singular perturbations in parabolic problems subjected to nonlinear Neumann boundary conditions. We consider the case for which the diffusion coefficient blows up in a subregion Ω0 which is interior to the physical domain Ω⊂Rn. We prove, under natural assumptions, that the associated attractors behave continuously as the diffusion coefficient blows up locally uniformly in Ω0 and converges uniformly to a continuous and positive function in  . |
| Keywords: | Parabolic equations Attractors Compact convergence Hyperbolic equilibrium Nonlinear boundary conditions |
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