Asymptotics, Stability, and Region of Attraction of Periodic Solution to a Singularly Perturbed Parabolic Problem with Double Root of a Degenerate Equation
For a singularly perturbed parabolic problem with Dirichlet boundary conditions, the asymptotic decomposition of a solution periodic in time and with boundary layers near the ends of the segment where the degenerate equation has a double root is constructed and substantiated. The construction algorithm for the asymptotics and the behavior of the solution in the boundary layers turn out to differ significantly as compared to the case of a simple root of a degenerate equation. The stability of the periodic solution and its region of attraction are also studied.
Keywordssingularly perturbed reaction–diffusion equations asymptotic approximations periodic solutions boundary layers Lyapunov stability region of attraction
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- 4.Butuzov, V.F., Nefedov, N.N., Recke, L., and Schneider, K.R., On a singularly perturbed initial value problem in the case of a double root of the degenerate equation, Nonlinear Anal., 2012, pp. 1–11Google Scholar
- 7.Butuzov, V.F., Nefedov, N.N., Recke, L., and Schneider, K.R., Periodic solutions with a boundary layer of reaction-diffusion equations with singularly perturbed Neumann boundary conditions, Int. J. Bif. Chaos, 2014, vol. 24.Google Scholar
- 8.Hess, P., Hess periodic-parabolic boundary value problems and positivity, Pitman Res. Notes Math. Ser., 1991, vol. 247.Google Scholar
- 9.Pao, C.V., Nonlinear Parabolic and Elliptic Equations, New York and London: Plenum Press, 2004.Google Scholar