On spectral convergence for some parabolic problems with locally large diffusion

Maria C. Carbinatto, Krzysztof P. Rybakowski

DOI: http://dx.doi.org/10.12775/TMNA.2018.025

Abstract


In this paper, which is a sequel to \cite{CR11}, we extend the spectral convergence result from \cite{CP} to a larger class of singularly perturbed families of scalar linear differential operators. This also extends the Conley index continuation principles from \cite{CR11}.

Keywords


Spectral convergence; localized large diffusion; singular perturbations; Conley index

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References


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), no. 2, 741–755.

A.N. Carvalho, Infinite dimensional dynamics described by ordinary differential equations, J. Differential Equations 116 (1995), no. 2, 338–404.

A.N. Carvalho, J.W. Cholewa, G. Lozada-Cruz and M.R.T. Primo, Reduction of infinite dimensional systems to finite dimensions: Compact convergence approach, SIAM J. Math. Anal. 45 (2013), 600–638.

A.N. Carvalho and J.A. Cuminato, Reaction-diffusion problems in cell tissues, J. Dynam. Differential Equations 9 (1997), 93–131.

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.


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