Singularly perturbed two-dimensional parabolic problem in the case of intersecting roots of the reduced equation |
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Authors: | V F Butuzov |
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Institution: | (1) Faculty of Physics, Moscow State University, Leninskie gory, Moscow, 119992, Russia |
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Abstract: | The singularly perturbed parabolic equation ?u t + ε2Δu ? f(u, x, ε) = 0, x ∈ D ? ?2, t > 0 with Robin conditions on the boundary of D is considered. The asymptotic stability as t → ∞ and the global domain of attraction are analyzed for the stationary solution whose limit as ε → 0 is a nonsmooth solution to the reduced equation f(u, x, 0) = 0 that consists of two intersecting roots of this equation. |
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Keywords: | singularly perturbed equations asymptotic stability parabolic equations |
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