On the solvability of the Cauchy problem for a thermal-electrical model

We consider a thermal-electrical \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(3+1)$$\end{document}-dimensional model of semiconductor heating in an electric field. We prove the existence of a classical solution nonextendable in time for the corresponding Cauchy problem.