An application of a nonlinear integral equation for finding the asymptotics of a solution of a nonlinear heat equation (Q2459744)

A nonlinear parabolic equation that describes two-dimensional nonstationary temperature fields in pulse energy output window of microwave devices with given initial and boundary conditions is considered. The nonlinearities model radiation cooling by the Stefan-Boltzmann law, heating by internal heat sources by a power law, and the linear dependence of the heat conductivity on temperature. The author suggests a method for deriving the Poincaré asymptotics of solutions to the Cauchy problem for the considered nonlinear heat equation. To derive the asymptotics of the solutions to the Cauchy problem, he performs an asymptotic analysis of the solutions of the equivalent nonlinear integral equation.