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Fundamental solution of a loaded second-order parabolic equation with constant coefficients

  • Partial Differential Equations
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Abstract

We study a second-order partial differential equation containing fractional derivatives with respect to one of the two independent variables. We construct a fundamental solution of this equation, analyze its properties, and derive a general representation of solutions in a rectangular domain. It follows from this representation that the presence of a lower fractional derivative in the equation may affect the well-posedness of initial and initial–boundary value problems.

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Authors and Affiliations

  1. Institute for Applied Mathematics and Automation, Kabardino-Balkar Scientific Center, Russian Academy of Sciences, Nal’chik, Russia

    M. O. Mamchuev

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  1. M. O. Mamchuev
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Correspondence to M. O. Mamchuev.

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Original Russian Text © M.O. Mamchuev, 2015, published in Differentsial’nye Uravneniya, 2015, Vol. 51, No. 5, pp. 611–620.

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Mamchuev, M.O. Fundamental solution of a loaded second-order parabolic equation with constant coefficients. Diff Equat 51, 620–629 (2015). https://doi.org/10.1134/S0012266115050055

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  • DOI: https://doi.org/10.1134/S0012266115050055

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