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Weak Solvability of the Variable-Order Subdiffusion Equation

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Abstract

In this work, we study a new type of linear partial differential equations–the variable-order subdiffusion equation. Here the Laplace operator in space acts on the Riemann-Liouville time derivative of space-dependent order. We construct a variable-order Sobolev and prove the weak solvability of the initial-boundary value problem for this equation, which confirms the well-posedness of the problem. Finally, we briefly discuss the application of the developed approach to the more general variable-order reaction-subdiffusion equation.

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  1. Faculty of Computer Science and Cybernetics, Taras Shevchenko National University of Kyiv, 4d, Glushkov Avenue, Kyiv -, 03680, Ukraine

    Andrii Hulianytskyi

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  1. Andrii Hulianytskyi
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Hulianytskyi, A. Weak Solvability of the Variable-Order Subdiffusion Equation. Fract Calc Appl Anal 23, 920–934 (2020). https://doi.org/10.1515/fca-2020-0047

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  • DOI: https://doi.org/10.1515/fca-2020-0047

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