Solvability of the First Boundary-Value Problem for the Heat-Conduction Equation with Nonlinear Sources and Strong Power Singularities

Abstract

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.