Hyperbolic Conservation Laws An Illustrated Tutorial (PDF 81P)
Hyperbolic Conservation Laws An Illustrated Tutorial (PDF 81P)
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
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
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.
This note covers the following topics: Hyperbolic conservation
laws, stability of hyperbolic waves, heat equation, burgers waves, burgers
greens functions, stability of diffusion waves, stability of shock waves,
estimates of the greens function, stability of rarefaction waves, stability of
rarefaction waves.
Author(s): Tai-ping Liu, Shih-hsien Yu
and Yanni Zeng
This note covers the following topics: Conserved Quantities, Energy and Momentum, Charge, Angular Momentum, Particle
categories, Leptons and Lepton Number, Baryons and Baryon Number.