IUMJ

Title: Heat Flow with Shocks in Media with Memory

Authors: Constantine Dafermos

Issue: Volume 62 (2013), Issue 5, 1443-1456

Abstract:

The Cauchy problem for the system of nonlinear integrodifferential conservation laws governing heat flow in one-di\-men\-sional media with memory is solved in the class of $BV$ functions, supporting shock waves in the temperature gradient. The solution is attained with the help of a change of variables that redistributes the damping equitably between the two equations of the system.