Lecture Notes on Hyperbolic Conservation Laws

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

Aspects Of Symmetry (PDF 26P)

This note covers the following topics: introduction, conservation laws, the wheatstone bridge electric circuit, the golden ratio, embryonic development.

Author(s): Opal Boonpitak, Ji-in Choi, Katie Kemp, Noa Krugliak, Ilya Mohedano, Rebecca Ranay, Lidija Relja, Anam Shaikh, Lily Simmons, Keila Valle, And Monica J. Wojciechowski

26 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

Class Notes Conservation Laws

This note covers the following topics: Conserved Quantities, Energy and Momentum, Charge, Angular Momentum, Particle categories, Leptons and Lepton Number, Baryons and Baryon Number.

Author(s): Maurice Barnhill

NA Pages