Renormalized entropy solutions to the Cauchy problem for first order quasilinear conservation laws in the class of periodic functions

We introduce the notion of a periodic in spatial variables renormalized entropy solution to the Cauchy problem for a first order quasilinear conservation law. We prove the existence and uniqueness theorems and comparison principle. We also clarify relations with generalized entropy solutions. Bibliography: 19 titles. Illustrations: 1 figure.