On the Existence of a Nonextendable Solution of the Cauchy problem for a(1+1)-Dimensional Thermal-Electrical Model

We consider one thermal-electrical(1 + 1)-dimensional model of heating a semiconduc-torinanelectricfield. For the corresponding Cauchy problem, we prove the existence of a classicalsolution nonextendable in time and obtain a global-in-time a priori estimate.