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Localized Blow-Up Regimes for Quasilinear Doubly Degenerate Parabolic Equations

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Abstract

Singular blow-up regimes are studied for a wide class of second-order quasilinear parabolic equations. Energy methods are used to obtain exact (in a certain sense) estimates of the final profile of the generalized solution near the blow-up time depending on the rate of increase of the global energy of this solution.

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Funding

The work of the first-named author was supported by the “5–100” program of RUDN University.

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Authors and Affiliations

  1. RUDN University, Moscow, 117198, Russia

    A. E. Shishkov

  2. Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Slavyansk, 84116, Ukraine

    A. E. Shishkov & Ye. A. Yevgenieva

Authors
  1. A. E. Shishkov
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  2. Ye. A. Yevgenieva
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Corresponding authors

Correspondence to A. E. Shishkov or Ye. A. Yevgenieva.

Additional information

Russian Text © The Author(s), 2019, published in Matematicheskie Zametki, 2019, Vol. 106, No. 4, pp. 622–635.

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Shishkov, A.E., Yevgenieva, Y.A. Localized Blow-Up Regimes for Quasilinear Doubly Degenerate Parabolic Equations. Math Notes 106, 639–650 (2019). https://doi.org/10.1134/S000143461909030X

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  • DOI: https://doi.org/10.1134/S000143461909030X

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