Abstract
The Cauchy problem for non-uniformly 2b-parabolic equations with degenerations is investigated. Coefficients of parabolic equations can have power singularities of arbitrary order with respect to any variables on some set of points. Using prior estimates and Arzelа’s and Riesz’s theorems the existence and integral representation of the unique solution to the formulated Cauchy problem are established. Estimates for the solution of the Cauchy problem and its derivatives in Hölder spaces with power weight are found. The order of the power weight is defined in terms of orders of the power singularities and degenerations in coefficients of 2b-parabolic equations. Cite as: І. P. Medynsky, “Fundamental solutіons for degenerate parabolіc equatіons: existence, propertіes and some theіr applіcatіons,” Mat. Met. Fiz.-Mekh. Polya , 64 , No. 2, 31–41 (2021) (in Ukrainian), https://doi.org/10.15407/mmpmf2021.64.2.31-41
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