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Time asymptotic behavior of the solution to a quasilinear parabolic equation

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Abstract

The time asymptotic behavior of the solution to the Cauchy problem for a quasilinear parabolic equation is analyzed. Such problems are encountered, for example, in gas dynamics and transport flow simulation. A.M. Il’in and O.A. Oleinik’s well-known results are extended to a wider class of equations in which the time derivative of the unknown function is multiplied by a fixed-sign function of the former. The results have found applications in mathematical economics.

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Authors and Affiliations

  1. Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119991, Russia

    A. V. Gasnikov

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  1. A. V. Gasnikov
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Original Russian Text © A.V. Gasnikov, 2006, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2006, Vol. 46, No. 12, pp. 2235–2253.

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Gasnikov, A.V. Time asymptotic behavior of the solution to a quasilinear parabolic equation. Comput. Math. and Math. Phys. 46, 2136–2153 (2006). https://doi.org/10.1134/S0965542506120128

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  • DOI: https://doi.org/10.1134/S0965542506120128

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