The propagation of disturbances in problems of non-linear heat conduction with absorption

Abstract THE CAUCHY problem is considered for the equation of non-linear heat conduction with heat absorption. For the case of a finite initial temperature distribution, we find the conditions under which no heat penetrates beyond a finite domain; and we show that these condtions are almost necessary. In the case of an arbitrary initial temperature distribution, we obtain criteria for total cooling in a finite time.