By using the maximum principle and a priori estimates, we study the first boundary-value problem for a linear parabolic equation with power singularities in coefficients with respect to the space variables and impulsive conditions with respect to the time variable. In Hölder spaces with power weights, we establish the existence and uniqueness of the solution of the posed problem.
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 58, No. 2, pp. 55–63, April–June, 2015.
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Pukal’s’kyi, І.D. Boundary-Value Problem for Parabolic Equations with Impulsive Conditions and Degenerations. J Math Sci 223, 60–71 (2017). https://doi.org/10.1007/s10958-017-3338-z
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DOI: https://doi.org/10.1007/s10958-017-3338-z