Hyperbolic Problems

by Tadmor, Eitan; Liu, Jian-guo; Tzavaras, Athanasios E.

• ISBN13: 9780821847282
• ISBN10: 0821847287
• Format: Hardcover
• Copyright: 2009-12-29
• Publisher: Amer Mathematical Society

Summary

Part I: List of plenary talks: Multidimensional shock waves and surface waves by S. Benzoni-Gavage and J.-F. Coulombel Shock reflection-diffraction phenomena and multidimensional conservation laws by G.-Q. Chen and M. Feldman Study on Mach reflection and Mach configuration by S. Chen Nonlinear regularizing effect for conservation laws by F. Golse Numerical methods for hyperbolic systems with singular coefficients: Well-balanced scheme, Hamiltonian preservation, and beyond by S. Jin Some recent results on the critical surface quasi-geostrophic equation: A review by A. Kiselev Why hyperbolic and kinetic models for cell populations self-organization? by B. Perthame Flows on networks and complicated domains by B. Piccoli Invited talks: Global solutions for a hyperbolic model of multiphase flow by D. Amadori and A. Corli On the convergence rate for the Glimm scheme by F. Ancona and A. Marson Analysis and computation for the semiclassical limits of the ground and excited states of the Gross-Pitaevskii equation by W. Bao and F. Y. Lim Conservation laws: Transonic flow and differential geometry by G.-Q. Chen, M. Slemrod, and D. Wang A survey on the $L^1$ comparison of entropy weak solutions to Euler equations in the large with respect to physical parameters by C. Christoforou Low regularity solutions of the Maxwell-Dirac system by P. D'Ancona, D. Foschi, and S. Selberg Stabilization for discontinuous Galerkin methods applied to systems of conservation laws by A. Dedner and R. Klofkorn Ill-posedness for bounded admissible solutions of the 2-dimensional $p$-system by C. De Lellis Applications of dispersive estimates to the acoustic pressure waves for incompressible fluid problems by D. Donatelli and P. Marcati Stability in the $L^1$ norm via a linearization method for nonlinear hyperbolic systems by P. G. LeFloch A review of semiconductor models: Global solvability and hierarchy by S. Nishibata and M. Suzuki Index Part II: Contributed talks: Two-dimensional transport equation with Hamiltonian vector fields by G. Alberti, S. Bianchini, and G. Crippa Analytic regularization of an inverse problem for a system of conservation laws by A. C. Alvarez, G. Hime, and D. Marchesin On the finite weak solutions to a system in quantum fluid dynamics by P. Antonelli and P. Marcati Accuracy of modeling error estimates for discrete velocity models by K. C. Assi and M. Laforest The Riemann solution for three-phase flow in a porous medium by A. V. Azevedo, A. P. de Souza, F. Furtado, and D. Marchesin Non-oscillatory central schemes for 3D hyperbolic conservation laws by J. Balbas and X. Qian A conservative, positivity preserving scheme for advection-diffusion-reaction equations in biochemical applications by J. Benz, A. Meister, and P. A. Zardo On the spectrum of a rank two modification of a diagonal matrix for linearized fluxes modelling polydisperse sedimentation by S. Berres and T. Voitovich Invariant manifolds for viscous profiles of a class of mixed hyperbolic-parabolic systems by S. Bianchini and L. V. Spinolo Nonlinear iterative solvers for unsteady Navier-Stokes equations by P. Birken and A. Jameson An approximate Riemann solver for ideal MHD based on relaxation by F. Bouchut, C. Klingenberg, and K. Waagan Numerical solution of an inverse problem for a scalar conservation law modelling sedimentation by R. Burger, A. Coronel, and M. Sepulveda A conservation law with discontinuous flux modelling traffic flow with abruptly changing road surface conditions by R. Burger, K. H. Karlsen, and J. D. Towers Numerical investigation of finite difference schemes for nonconservative hyperbolic systems by M. J. Castro-Diaz, P. G. LeFloch, M. L. Munoz-Ruiz, and C. Pares Relaxed schemes for nonlinear evolutionary PDEs by F. Cavalli, G. Naldi, G. Puppo, and M. Semplice Global asymptotic effects of the structure of combustion waves in porous media by G. Chapiro, G. Hime, A. Mailybaev, D. Marchesin, and A. P. de Souza Multiscale dynamics of 2D rotational compressi

Table of Contents

List of plenary talks

Multidimensional shock waves and surface waves

Shock reflection-diffraction phenomena and multidimensional conservation laws

Study on Mach reflection and Mach configuration

Nonlinear regularizing effect for conservation laws

Numerical methods for hyperbolic systems with singular coefficients: Well-balanced scheme, Hamiltonian preservation, and beyond

Some recent results on the critical surface quasi-geostrophic equation: A review

Why hyperbolic and kinetic models for cell populations self-organization?

Flows on networks and complicated domains

Invited talks: Global solutions for a hyperbolic model of multiphase flow

On the convergence rate for the Glimm scheme

Analysis and computation for the semiclassical limits of the ground and excited states of the Gross-Pitaevskii equation

Conservation laws: Transonic flow and differential geometry

A survey on the $L^1$ comparison of entropy weak solutions to Euler equations in the large with respect to physical parameters

Low regularity solutions of the Maxwell-Dirac system

Stabilization for discontinuous Galerkin methods applied to systems of conservation laws

Ill-posedness for bounded admissible solutions of the 2-dimensional $p$-system

Applications of dispersive estimates to the acoustic pressure waves for incompressible fluid problems

Stability in the $L^1$ norm via a linearization method for nonlinear hyperbolic systems

A review of semiconductor models: Global solvability and hierarchy

Index

Contributed talks

Two-dimensional transport equation with Hamiltonian vector fields

Analytic regularization of an inverse problem for a system of conservation laws

On the finite weak solutions to a system in quantum fluid dynamics

Accuracy of modeling error estimates for discrete velocity models

The Riemann solution for three-phase flow in a porous medium

Non-oscillatory central schemes for 3D hyperbolic conservation laws

A conservative, positivity preserving scheme for advection-diffusion-reaction equations in biochemical applications

On the spectrum of a rank two modification of a diagonal matrix for linearized fluxes modelling polydisperse sedimentation

Invariant manifolds for viscous profiles of a class of mixed hyperbolic-parabolic systems

Nonlinear iterative solvers for unsteady Navier-Stokes equations

An approximate Riemann solver for ideal MHD based on relaxation

Numerical solution of an inverse problem for a scalar conservation law modelling sedimentation

A conservation law with discontinuous flux modelling traffic flow with abruptly changing road surface conditions

Numerical investigation of finite difference schemes for nonconservative hyperbolic systems

Relaxed schemes for nonlinear evolutionary PDEs

Global asymptotic effects of the structure of combustion waves in porous media

Multiscale dynamics of 2D rotational compressible Euler equations-An analytic approach

Finite volume methods on unstructured Voronoi meshes for hyperbolic conservation laws

On the continuum modeling of crowds

Balance laws as quasidifferential equations in metric spaces

Simulation of rain-water overland-flow

On the vanishing viscosity approximation in the vectorial case

Counterexamples to the sonic and detachment criteria

Well-balanced high order scheme for 2-layer shallow water flows

High-order finite volume schemes for wave propagation in stratified atmospheres

High-order finite volume schemes for shallow water equations with topography and dry areas

Riemann solvers for conservation laws at a node

Reduced basis method for explcit finite volume approximations of nonlinear conservation laws

Error estimate for the local discontinuous Galerkin scheme of a diffusive-dispersive equation with convolution

Cauchy problem for capillarity Van der Vaals model

Viscous conservation laws with discontinuous initial data

Parallel computation of large amplitude shocks for a system of conservation laws with small data

Convergence of front tracking and the Glimm scheme for a model of the flow of immiscible gases

Global existence and incompressible limit of weak solutions to the multi-dimensional compressible magnetohydrodynamics

Construction of conservative systems

Collisionless magnetic reconnection in a five-moment two-fluid electron-positron plasma

Finite difference scheme for a nonlinear damped wave equation derived from brain modulation

Convergent finite element methods for compressible barotropic Stokes systems

A hybrid scheme for flows in porous media

Two-layer shallow water system and its applications

Asymptotic rarefaction waves for balance laws with stiff sources

Comparison of staggered and cell-centered Lagrangian and ALE hydrodynamical methods

On the entropy stability of Roe-type finite volume methods

Entropy stability of Roe-type upwind finite volume methods on unstructured grids

A robust high order VFRoe scheme for shallow water equations

Vorticity preserving schemes using potential-based fluxes for the system wave equation

Half space problem for the compressible Navier-Stokes equation

Computing the effective Hamiltonian for a time-dependent Hamiltonian

Initial boundary value problems for compressible Euler equations with damping

A relaxation method for modeling two-phase shallow granular flows

Riemann problem for Born-Infeld systems

Stability of traveling waves in thin liquid films driven by gravity and surfactant

Piecewise parabolic method on a local stencil for hyerbolic conservation laws

A numerical study of magnetic reconnection: A central scheme for Hall MHD

Accuracy of stabilized residual distribution for shallow water flows including dry beds

Using the entropy production rate to enhance aritificial compression

Blow up of smooth solutions to the barotropic compressible magnetohydrodynamic equations with finite mass and energy

High order well balanced schemes for systems of balance laws

Transport of mass, momentum and energy in zero-pressure gas dynamics

On a model of granular flow

A simple unified coordinates method for compressible homogeneous two-phase flows

Courant-Friedrich's hypothesis and stability of the weak shock

Unstaggered central schemes for MHD and SMHD

Stability of planar stationary wave for damped wave equation with nonlinear convection in half space

The minimum entropy approximation to the radiative transfer equation

Index

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