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Extinction of solutions of higher order parabolic equations with double nonlinearity and degenerate absorption potential

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Abstract

We study the extinction property of solutions to the Cauchy–Dirichlet problem for nonlinear parabolic equations of the order 2m with absorption potential in a semibounded cylinder (0,+∞) × Ω, where Ω is a bounded domain in ℝN, N ≥ 1. The sufficient conditions ensuring the extinction of a solution in a finite time, which depend on N,m, and q (where q is a parameter of the homogeneous nonlinearity in the main part of the equation), are obtained.

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Authors and Affiliations

  1. Institute of Applied Mathematics and Mechanics of the NAS of Ukraine, 74, R. Luxemburg Str., Donetsk, 83114, Ukraine

    Kateryna V. Stiepanova

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  1. Kateryna V. Stiepanova
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Correspondence to Kateryna V. Stiepanova.

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Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 11, No. 2, pp. 250–273, April–May, 2014.

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Stiepanova, K.V. Extinction of solutions of higher order parabolic equations with double nonlinearity and degenerate absorption potential. J Math Sci 204, 351–368 (2015). https://doi.org/10.1007/s10958-014-2207-2

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  • DOI: https://doi.org/10.1007/s10958-014-2207-2

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