A note on Conley index and some parabolic problems with locally large diffusion
Keywords
Conley index, homology index braids, localized large diffusion, singular perturbationsAbstract
We prove singular Conley index continuation results for a class of scalar parabolic equations with locally large diffusion considered by Fusco \cite{F} and Carvalho and Pereira \cite{CP}.References
M.C. Carbinatto and K.P. Rybakowski, Continuation of the connection matrix in singular perturbation problems, Ergodic Theory Dynam. Systems 26 (2006), 1021–1059.
M.C. Carbinatto and K.P. Rybakowski, Localized singularities and Conley index, Topol. Methods Nonlinear Anal. 37 (2011), 1–36.
M.C. Carbinatto and K.P. Rybakowski, On convergence and compactness in parabolic problems with globally large diffusion and nonlinear boundary conditions, Topol. Methods Nonlinear Anal. 40 (2012), 1–28.
A.N. Carvalho and J. Hale, Large diffusion with dispersion, Nonlinear Anal. 17 (1991), 1139–1151.
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.
C.C. Conley, Isolated Invariant Sets and the Morse Index, CBMS Amer. Math. Soc., vol. 38, Providence, 1978.
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.
J. Hale, Large diffusivity and asymptotic behavior in parabolic systems, J. Math. Anal. Appl. 118 (1986), 455–466.
J. Hale and C. Rocha, Varying boundary conditions with large diffusivity, J. Math. Pures Appl. 66 (1987), 139–158.
A. Rodrı́guez-Bernal, Localized spatial homogenization and large diffusion, SIAM J. Math. Anal. 29 (1998), 1361–1380.
A. Rodrı́guez-Bernal and R. Willie, Singular large diffusivity and spatial homogenization in a non homogeneous linear parabolic equation, Discrete Contin. Dyn. Syst. Ser. B 5 (2005), 385–409.
K.P. Rybakowski, On the homotopy index for infinite-dimensional semiflows, Trans. Amer. Math. Soc. 269 (1982), 351–382.
Published
How to Cite
Issue
Section
Stats
Number of views and downloads: 0
Number of citations: 0
