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Verification of asymptotic solutions for one-dimensional nonlinear parabolic equations

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Abstract

The present article proves a result that is new for partial differential equations. According to this result, the solution of the Cauchy problem for a nonlinear parabolic equation with variable, slowly changing coefficients will turn into (asymptotically approach) a special asymptotic solution, either a solution or a kink, for high values of t.

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Authors and Affiliations

  1. St. Petersburg Institute of Mechanical Engineering, Russian Academy of Sciences, USSR

    S. A. Vakulenko

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  1. S. A. Vakulenko
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Translated from Matematicheskie Zametki, Vol. 52, No. 3, pp. 10–16, September, 1992.

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Vakulenko, S.A. Verification of asymptotic solutions for one-dimensional nonlinear parabolic equations. Math Notes 52, 875–880 (1992). https://doi.org/10.1007/BF01209606

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  • DOI: https://doi.org/10.1007/BF01209606

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