Hyperbolic Conservation Laws An Illustrated Tutorial (PDF 81P)

Overview & Synopsis

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: Meaning
of a conservation equation and definition of weak solutions, Hyperbolic systems,
Shock waves: Rankine-Hugoniot equations and admissibility,Genuinely nonlinear
and linearly degenerate characteristic fields, Centered rarefaction waves,The
general solution of the Riemann problem, Wave interaction estimates,Weak
solutions to the Cauchy problem, with initial data having small total variation,
Approximations generated by the front-tracking method and by the Glimm scheme, Vanishing
viscosity approximations.