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On the Continuity of Solutions of the Equations of a Porous Medium and the Fast Diffusion with Weighted and Singular Lower-Order Terms

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Abstract

For the parabolic equation v(x)ut −  div (ω(x)um − 1 ∇ u) = f(x, t), u ≥ 0, m ≠ 1 we prove the continuity and the Harnack inequality for generalized k solutions, by using the weighted Riesz potential on the right-hand side of the equation.

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  1. Institute of Applied Mathematics and Mechanics of the NAS of Ukraine, Slov’yans’k, Ukraine

    Yevhen S. Zozulia

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Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 18, No. 1, pp. 104–139, January–March, 2021.

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Zozulia, Y.S. On the Continuity of Solutions of the Equations of a Porous Medium and the Fast Diffusion with Weighted and Singular Lower-Order Terms. J Math Sci 256, 803–830 (2021). https://doi.org/10.1007/s10958-021-05462-8

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