Heat Flow with Shocks in Media with Memory C. Dafermos 35L65Heat flowHyperbolic balance laws with memoryRedistribution of Damping 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. Indiana University Mathematics Journal 2013 text pdf 10.1512/iumj.2013.62.5126 10.1512/iumj.2013.62.5126 en Indiana Univ. Math. J. 62 (2013) 1443 - 1456 state-of-the-art mathematics http://iumj.org/access/