On the stability and domain of attraction of asymptotically nonsmooth stationary solutions to a singularly perturbed parabolic 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: | A stationary solution to the singularly perturbed parabolic equation ?u t + ε2 u xx ? f(u, x) = 0 with Neumann boundary conditions is considered. The limit of the solution as ε → 0 is a nonsmooth solution to the reduced equation f(u, x) = 0 that is composed of two intersecting roots of this equation. It is proved that the stationary solution is asymptotically stable, and its global domain of attraction is found. |
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| Keywords: | singularly perturbed parabolic equations boundary value problem asymptotic method of solving stable solutions |
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