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On long-time asymptotics of solutions of parabolic equations with increasing leading coefficients

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Abstract

Sharp sufficient conditions on the coefficients of a second-order parabolic equation are examined under which the solution of the corresponding Cauchy problem with a power-law growing initial function stabilizes to zero. An example is presented showing that the found sufficient conditions are sharp. Conditions on the coefficients of a parabolic equation are obtained under which the solution of the Cauchy problem with a bounded initial function stabilizes to zero at a power law rate.

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Authors and Affiliations

  1. Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119992, Russia

    V. N. Denisov

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  1. V. N. Denisov
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Correspondence to V. N. Denisov.

Additional information

Original Russian Text © V.N. Denisov, 2017, published in Doklady Akademii Nauk, 2017, Vol. 475, No. 1, pp. 10–13.

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Denisov, V.N. On long-time asymptotics of solutions of parabolic equations with increasing leading coefficients. Dokl. Math. 96, 308–311 (2017). https://doi.org/10.1134/S1064562417040020

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  • DOI: https://doi.org/10.1134/S1064562417040020

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