Regularity of solutions to the perturbed conservation laws

Abstract

A kind of regularity for the mild solution of perturbed conservation laws is proposed. This regularity is described in term of variations measured in the L1-norm. A dissipativity condition from the semigroup approach is used to show that the mild solution stays within a class of bounded variation in this sense of regularity. This shows that this class of functions is an invariant of the semigroup. The same analysis carries over to the periodic problem. The class of boundedL1-variation functions used here can be normed to give a Banach space structure. It also has an analogue with the space of Lipschitz functions