Hyperbolic Conservation Laws An Illustrated Tutorial (PDF 81P)

Numerical methods for conservation laws and related equations

These notes present numerical methods for conservation laws and related time dependent nonlinear partial differential equations. The focus is on both simple scalar problems as well as multi dimensional systems.

Author(s): Siddhartha Mishra

103 Pages

Lecture Notes on Hyperbolic Conservation Laws

These notes provide an introduction to the theory of hyperbolic systems of conservation laws in one space dimension.

Author(s): Alberto Bressan

84 Pages

Hyperbolic Conservation Laws An Illustrated Tutorial (PDF 81P)

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.

Author(s): Alberto Bressan,Department of Mathematics, Penn State University

81 Pages

Applications Of Variational Principles To Dynamics And Conservation Laws In Physics (PDF 24P)

This note covers the following topics: introduction, calculus of variations basics, the action, Lagrangian and lagrangian density, particles, fields, canonical variables, the euler-lagrange equations and dynamics in particles, fields, Noether's theorem and conservation laws.

Author(s): Daniel J Older

24 Pages