Entropy solutions and renormalized entropy solutions for degenerate problems.

Abstract

This conference contribution gives a brief introduction to the resolution of some degenerate problems with the L1 theory in open bounded sets. The first part of the work describes well known concepts related to entropy solutions of Kruzhkov and results ensuring existence for data and initial conditions in L1. In the second part, the author introduces the concept of renormalized entropy solutions and gives an existence and uniqueness result for such solution when data and initial condition are in L1. The work ends with a short history of renormalized solutions.