We consider the second boundary-value problem for a parabolic equation with power singularities in the coefficients of space variables and impulsive conditions in the time variable. By using the maximum principle and a priori estimates, we establish the existence and uniqueness of the solution of posed problem in Hölder spaces with power weights.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 10, pp. 1348–1357, October, 2015.
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Isaryuk, I.M., Pukal’s’kyi, I.D. Boundary-Value Problem with Impulsive Conditions and Degeneration for Parabolic Equations. Ukr Math J 67, 1515–1526 (2016). https://doi.org/10.1007/s11253-016-1169-6
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DOI: https://doi.org/10.1007/s11253-016-1169-6