Notes on Hyperbolic Conservation Laws

  title={Notes on Hyperbolic Conservation Laws},
  author={Alberto Bressan},
These notes provide an introduction to the theory of hyperbolic systems of conservation laws in one space dimension. The various chapters cover the following topics: 1. Meaning of the conservation equations and definition of weak solutions. 2. Shocks, Rankine-Hugoniot equations and admissibility conditions. 3. Genuinely nonlinear and linearly degenerate characteristic fields. Solution to the Riemann problem. Wave interaction estimates. 4. Weak solutions to the Cauchy problem, with initial data… CONTINUE READING


Publications referenced by this paper.
Showing 1-10 of 48 references

Solutions in the large for nonlinear hyperbolic systems of equations

J. Glimm
Comm. Pure Appl. Math. 18 • 1965
View 15 Excerpts
Highly Influenced

Convergence of approximate solutions to conservation laws

R. DiPerna
Arch. Rational Mech. Anal. 82 • 1983
View 4 Excerpts
Highly Influenced

The spaces BV and quasilinear equations

A. I. Volpert
Math. USSR Sbornik 2 • 1967
View 3 Excerpts
Highly Influenced

BV solutions to systems of conservation laws by vanishing viscosity

A. Bressan
C.I.M.E. course in Cetraro, 2003, P. Marcati ed. Springer Lecture Notes in Math. 1911 • 2007
View 1 Excerpt

Stability of front tracking solutions to the initial and boundary value problem for systems of conservation laws

C. Donadello, A. Marson
Nonlinear Differential Equations Appl. 14 • 2007
View 1 Excerpt