SHORT Course: Introduction to Hyperbolic Systems of Conservation Laws

by Pierangelo Marcati (GSSI)

Monday 13 Apr 2026, 10:45 → Friday 24 Apr 2026, 12:45 Europe/Rome

GSSI

Lecturer
Pierangelo Marcati pierangelo.marcati@gssi.it

Timetable and workload
Lectures: 12 hours

Course content

1.  Introduction, some general aspects.  Scalar Conservation Laws, Nonlinear elementary waves, Riemann problem, Lax and Oleinik theories, N-waves Kruzhkov approach
2. System of Conservation Laws-I. Lax and Liu Entropy conditions, Riemann Problem, Glimm Scheme (sketch) and Front Tracking, Liu functional
3. System of Conservation Laws -II.  Bianchini – Bressan Vanishing viscosity
4. Compensated Compactness 
5. Kinetic Approach
6. Overview of the current literature

 

Some notes will be provided.

 

Bibliography

Liu T.P.  Shock Waves AMS

Bressan A. Hyperbolic Systems of Conservation Laws: The One-dimensional Cauchy Problem, Oxford UP

Dafermos C.M. Hyperbolic Conservation Laws in Continuum Physics Springer

Lax P.D. Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves CBMS-NSF SIAM 

Smoller J.  Shock Waves and reaction Diffusion Equations Springer 

Perthame B. Kinetic Formulation of Conservation Laws  Oxford UP