Conley index continuation for a singularly perturbed periodic boundary value problem

Maria C. Carbinatto, Krzysztof P. Rybakowski

DOI: http://dx.doi.org/10.12775/TMNA.2019.023

Abstract


We establish spectral convergence and Conley index continuation results for a class of singularly perturbed periodic boundary value problems.

Keywords


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

Full Text:

PREVIEW FULL TEXT

References


H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Universitext, Springer, 2010.

M.C. Carbinatto and K.P. Rybakowski, A note on Conley index and some parabolic problems with locally large diffusion, Topol. Methods Nonlinear Anal. 50 (2017), 741–755.

M.C. Carbinatto and K.P. Rybakowski, On spectral convergence for some parabolic problems with locally large diffusion, Topol. Methods Nonlinear Anal. 52 (2018), 631–664.

A.N. Carvalho and A.L. Pereira, A scalar parabolic equation whose asymptotic behavior is dictated by a system of ordinary differential equations, J. Differential Equations 112 (1994), 81–130.

G. Fusco, On the explicit construction of an ODE which has the same dynamics as scalar parabolic PDE, J. Differential Equations 69 (1987), 85–110.


Refbacks

  • There are currently no refbacks.

Partnerzy platformy czasopism