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On the solvability of the Cauchy problem with growing initial data for a class of anisotropic parabolic equations

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Abstract

We study the Cauchy problem for a doubly nonlinear parabolic equation with anisotropic degeneration in the case where the initial data are locally finite Radon measures growing, generally saying, at infinity. The weak solution of the problem is obtained as the limit of regular solutions with smoothed initial data.

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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

    Sergei P. Degtyarev & Anatolii F. Tedeev

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  1. Sergei P. Degtyarev
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  2. Anatolii F. Tedeev
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Correspondence to Anatolii F. Tedeev.

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Translated from Russian by V. V. Kukhtin

Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 8, No. 3, pp. 365–380, July–August, 2011.

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Degtyarev, S.P., Tedeev, A.F. On the solvability of the Cauchy problem with growing initial data for a class of anisotropic parabolic equations. J Math Sci 181, 28–46 (2012). https://doi.org/10.1007/s10958-012-0674-x

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  • DOI: https://doi.org/10.1007/s10958-012-0674-x

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