Chmyr O. Yu.
Solvability of the First Boundary-Value Problem for the Heat-Conduction Equation with Nonlinear Sources and Strong Power Singularities
Ukr. Mat. Zh. - 2013. - 65, № 10. - pp. 1388–1407
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.