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On the instantaneous shrinking of the support of a solution to the Cauchy problem for an anisotropic parabolic equation

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Ukrainian Mathematical Journal Aims and scope

We study the phenomenon of instantaneous shrinking of the support of solution to the Cauchy problem for the parabolic equation with anisotropic degeneration, double nonlinearity, and strong absorption. In terms of the behavior of locally integrable initial data, we formulate necessary and sufficient conditions for the realization of instantaneous shrinking and establish the exact (in order) bilateral estimates for the size of the support of solution.

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Authors and Affiliations

  1. Institute of Applied Mathematics and Mechanics, Ukrainian National Academy of Sciences, Donetsk, Ukraine

    S. P. Degtyarev

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  1. S. P. Degtyarev
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 5, pp. 625–640, May, 2009.

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Degtyarev, S.P. On the instantaneous shrinking of the support of a solution to the Cauchy problem for an anisotropic parabolic equation. Ukr Math J 61, 747–763 (2009). https://doi.org/10.1007/s11253-009-0246-5

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  • DOI: https://doi.org/10.1007/s11253-009-0246-5

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