# A tutorial on hyperbolic conservation laws. Lecture 1

Monday, July 13, 2009 - 3:30pm - 4:45pm

EE/CS 3-180

Alberto Bressan (The Pennsylvania State University)

This set of lectures will provide a basic introduction to

hyperbolic systems of conservation laws in one space dimension.

The main topics covered will be:

hyperbolic systems of conservation laws in one space dimension.

The main topics covered will be:

- Meaning of the conservation equations and

definition of weak solutions. - Shocks, Rankine-Hugoniot equations and admissibility

conditions. - The Riemann problem. Wave interaction estimates.
- Weak solutions to the Cauchy problem with small BV data.
- Uniqueness and continuous dependence.
- Vanishing viscosity approximations.
- Some counter-examples to global existence,

uniqueness, and continuous dependence of solutions,

when some key hypotheses are removed.

MSC Code:

35L65

Keywords: