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Method of energy estimates for the study of a behavior of weak solutions of the equation of slow diffusion with singular boundary data

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Abstract

The equation of slow diffusion with singular boundary data is considered. An estimate of all weak solutions of such a problem is obtained, provided that the boundary regime is localized. The comparative analysis of the results obtained by the method of energy estimates and the barrier technique for the equation of porous medium is presented.

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Authors and Affiliations

  1. Institute of Applied Mathematics and Mechanics of the NAS of Ukraine, Slov’yans’k, Ukraine

    Yevgeniia A. Yevgenieva & Andrey E. Shishkov

  2. Peoples’ Friendship University of Russia, Moscow, Russia

    Andrey E. Shishkov

Authors
  1. Yevgeniia A. Yevgenieva
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  2. Andrey E. Shishkov
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Correspondence to Yevgeniia A. Yevgenieva.

Additional information

The article is dedicated to the centenary from the birthday of G. D. Suvorov

Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 16, No. 2, pp. 277–288 April–June, 2019.

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Yevgenieva, Y.A., Shishkov, A.E. Method of energy estimates for the study of a behavior of weak solutions of the equation of slow diffusion with singular boundary data. J Math Sci 244, 95–103 (2020). https://doi.org/10.1007/s10958-019-04606-1

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  • DOI: https://doi.org/10.1007/s10958-019-04606-1

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