Analysis and Numerical Simulation of the Initial–Boundary Value Problem for Quasilinear Equations of Complex Heat Transfer

Abstract

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.