  We model the operative treatment of incompetent truncal veins using
endovenous laser ablation (EVLA). Three differential equations, namely the
diffusion, the heat and the bioheat equations, are considered in the
endovenous-perivenous multidomain, describing the lumen, the vein wall, the
tissue pad and the skin. Exact solutions are provided. Our main concern is to
accurate the heat source by taking the Beer--Lambert law into account in the
irradiance of the incident beam. To accurate the heat transfer at the skin
boundary, the Newton law of cooling is considered as a Robin boundary
condition. Open problems are presented.
