We prove singular Conley index continuation results for a class of scalar parabolic equations with locally large diffusion considered by Fusco [On the explicit construction of an ODE which has the same dynamics as scalar parabolic PDE, J. Differential Equations 69 (1987), 85-110] and Carvalho and Pereira [A scalar parabolic equation whose asymptotic behavior is dictated by a system of ordinary differential equations, J. Differential Equations 112 (1994), 81-130].
"A note on Conley index and some parabolic problems with locally large diffusion." Topol. Methods Nonlinear Anal. 50 (2) 741 - 755, 2017. https://doi.org/10.12775/TMNA.2017.043