Mohamed MBEHOU
Summary: These notes are intended for first-year Master students. After having strengthened their knowledge on ordinary differential equations, students get in touch with partial differential equations and some of the methods and problems related to them. At the same time, it is hoped to strengthen the knowledge and skills of students in mathematical analysis. Learning basics techniques to solve first and second-order PDEs.
In these lecture notes, we will cover some relevant applications of scalar conservation laws. We focus mainly on local existence and smooth solution, Riemann problem for traffic flow and Burgers equations, weak antropy solution, Rankine Hugoniot condition.