Localized singularities and the Conley index

Maria C. Carbinatto, Krzysztof P. Rybakowski


We establish some abstract convergence and Conley index continuation
principles for families of singularly perturbed semilinear parabolic
equations and apply them to reaction-diffusion equations with nonlinear
boundary conditions and localized large diffusion. This extends and refines
previous results of [A. Rodriguez-Bernal, < i> Localized spatial homogenization and large
diffusion< /i> , SIAM J. Math. Anal. < b> 29< /b> (1998), 1361-1380] and
[J.M. Arrieta, A.N. Carvalho and A. Rodr\'{\i}guez-Bernal, < i> Parabolic problems with
nonlinear boundary conditions and critical nonlinearities< /i> ,
J. Differential Equations < b> 156< /b> (1999), 376-406].


Conley index; homology index braids; localized large diffusion; singular perturbations

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