Abstract
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, Localized spatial homogenization and large diffusion, SIAM J. Math. Anal. 29 (1998), 1361-1380] and [J.M. Arrieta, A.N. Carvalho and A. Rodríguez-Bernal, Parabolic problems with nonlinear boundary conditions and critical nonlinearities, J. Differential Equations 156 (1999), 376-406].
Citation
Maria C. Carbinatto. Krzysztof P. Rybakowski. "Localized singularities and the Conley index." Topol. Methods Nonlinear Anal. 37 (1) 1 - 35, 2011.
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