A conservation law is a first order partial differential equation suitable to describe phenomena of transport of some kind of mass, such as: fluid flow, gas 
dynamics, traffic flow, crowd dynamics, and many others. The presence of a term in the equation which models some memory effects (i.e.: the behavior of the mass 
at time t also depends on what happened in the past) is certainly interesting from a modeling as well as from an analytical point of view. In particular, the case 
when the memory effect presents a hysteresis feature (a particular kind of memory) is certainly worth studying.