Nonlinear Conservation Laws and Applications

by Bressan, Alberto; Chen, Gui-Qiang G.; Lewicka, Marta; Wang, Dehua

• ISBN13: 9781441995537
• ISBN10: 1441995536
• Format: Hardcover
• Copyright: 2011-05-03
• Publisher: Springer Verlag

Summary

This volume contains the proceedings of the Summer Program on Nonlinear Conservation Laws and Applications held at the IMA on July 13--31, 2009. Hyperbolic conservation laws is a classical subject, which has experienced vigorous growth in recent years. The present collection provides a timely survey of the state of the art in this exciting field, and a comprehensive outlook on open problems. Contributions of more theoretical nature cover the following topics: global existence and uniqueness theory of one-dimensional systems, multidimensional conservation laws in several space variables and approximations of their solutions, mathematical analysis of fluid motion, stability and dynamics of viscous shock waves, singular limits for viscous systems, basic principles in the modeling of turbulent mixing, transonic flows past an obstacle and a fluid dynamic approach for isometric embedding in geometry, models of nonlinear elasticity, the Monge problem, and transport equations with rough coefficients. In addition, there are a number of papers devoted to applications. These include: models of blood flow, self-gravitating compressible fluids, granular flow, charge transport in fluids, and the modeling and control of traffic flow on networks.

Table of Contents

Foreword	p. v
Preface	p. vii
General Survey Lectures
Open questions in the theory of one dimensional hyperbolic conservation laws	p. 1
Multidimensional conservation laws: Overview, problems, and perspective	p. 23
Mathematical analysis of fluids in motion	p. 73
Selected topics in approximate solutions of nonlinear conservation laws. High-resolution central schemes	p. 101
Stability and dynamics of viscous shock waves	p. 123
Specialized Research Lectures
Mathematical aspects of a model for granular flow	p. 169
The flow associated to weakly differentiable vector fields: recent results and open problems	p. 181
Existence and uniqueness results for the continuity equation and applications to the chromatography system	p. 195
Finite energy weak solutions to the quantum hydrodynamics system	p. 205
The Monge problem in geodesic spaces	p. 217
Existence of a unique solution to a nonlinear moving-boundary problem of mixed type arising in modeling blood flow	p. 235
Transonic flows and isometric embeddings	p. 257
Well posedness and control in models based on conservation laws	p. 267
Homogenization of nonlinear partial differential equations in the context of ergodic algebras: Recent results and open problems	p. 279
Conservation laws at a node	p. 293
Nonlinear hyperbolic surface waves	p. 303
Vacuum in gas and fluid dynamics	p. 315
On radially symmetric solutions to conservation laws	p. 331
Charge transport in an incompressible fluid: New devices in computational electronics	p. 353
Localization and shear bands in high strain-rateplasticity	p. 365
Hyperbolic conservation laws on spacetimes	p. 379
Reduced theories in nonlinear elasticity	p. 393
Mathematical, physical and numerical principles essential for models of turbulent mixing	p. 405
On the Euler-Poisson equations of self-gravitating compressible fluids	p. 415
Viscous system of conservation laws: Singular limits	p. 433
A two-dimensional Riemann problem for scalar conservation laws	p. 447
Semi-hyperbolic waves in two-dimensional compressible Euler systems	p. 457
IMA summer program participants	p. 469
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