RENORMALIZED ENTROPY SOLUTIONS TO THE CAUCHY PROBLEM FOR A QUASILINEAR FIRST ORDER EQUATION

摘要

We introduce the notion of a renormalized entropy solution to the Cauchy problem for a quasilinear first order equation with an arbitrary measurable initial function. The existence and uniqueness theorems are proved. We also prove the comparison principle and study relations between renormalized and generalized entropy solutions. We also establish the stability of a renormalized entropy solution with respect to summable perturbations of the initial data. Bibliography: 13 titles.