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On the stability and domain of attraction of asymptotically nonsmooth stationary solutions to a singularly perturbed parabolic equation

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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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Authors and Affiliations

  1. Faculty of Physics, Moscow State University, Leninskie gory, Moscow, 119992, Russia

    V. F. Butuzov

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  1. V. F. Butuzov
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Original Russian Text © V.F. Butuzov, 2006, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2006, Vol. 46, No. 3, pp. 433–444.

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Butuzov, V.F. On the stability and domain of attraction of asymptotically nonsmooth stationary solutions to a singularly perturbed parabolic equation. Comput. Math. and Math. Phys. 46, 413–424 (2006). https://doi.org/10.1134/S0965542506030080

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  • DOI: https://doi.org/10.1134/S0965542506030080

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