Analysis and numerical simulation of the initial-boundary value problem for quasilinear equations of complex heat transfer

We consider an initial-boundary value problem for quasilinear equations of complex heat transfer that model the process of endovenous laser ablation. A priori estimates for the solution are obtained. Results on the global unique solvability of the problem are presented. An algorithm for finding a solution of the initial-boundary value problem is proposed. The efficiency of the algorithm is illustrated by numerical examples. The influence of internal thermal radiation on the behavior of temperature fields is evaluated.