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Journal of Mathematical Sciences

, Volume 244, Issue 1, pp 95–103 | Cite as

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

  • Yevgeniia A. YevgenievaEmail author
  • Andrey E. Shishkov
Article
  • 4 Downloads

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.

Keywords

Quasilinear parabolic equations equation of porous medium method of energy estimates weak solutions singular boundary data 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Yevgeniia A. Yevgenieva
    • 1
    Email author
  • Andrey E. Shishkov
    • 1
    • 2
  1. 1.Institute of Applied Mathematics and Mechanics of the NAS of UkraineSlov’yans’kUkraine
  2. 2.Peoples’ Friendship University of RussiaMoscowRussia

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