ABSTRACT
This chapter addresses the issue of the global, in time, existence of weak solutions for the Cauchy problem governing the evolution of the current and charge distribution in a nonlinear, distributed parameter transmission line. It reviews those ideas of DiPerna which are connected with employing the concept of the Young measure, and the technique of compensated compactness, in order to establish the existence of global weak solutions for initial-value problems associated with strictly hyperbolic, genuinely nonlinear, homogeneous systems of conservation laws. To deal, in a precise manner, with the central issue of weak convergence, the concept of the Young measure is introduced in two different, albeit, related ways; the importance of being able to prove, in practical situations, that the Young measure which is generated by a sequence of solutions to a parabolically regularized hyperbolic equation is, in fact, a Dirac measure, is then illustrated by using the Burgers’ equation as an example once again.
