By using the Schauder principle and the principle of contracting mappings, we study the character of point power singularities for the solution of the generalized first boundary-value problem for the heat-conduction equation with nonlinear boundary conditions. We establish sufficient conditions for the solvability of the analyzed problem.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, No. 10, pp. 1388–1407, October, 2013.
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Chmyr, O.Y. Solvability of the First Boundary-Value Problem for the Heat-Conduction Equation with Nonlinear Sources and Strong Power Singularities. Ukr Math J 65, 1542–1565 (2014). https://doi.org/10.1007/s11253-014-0877-z
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DOI: https://doi.org/10.1007/s11253-014-0877-z