Cart
Free US shipping over $10
Proud to be B-Corp

Advances in the Theory of Shock Waves T.-P. Liu

Advances in the Theory of Shock Waves By T.-P. Liu

Advances in the Theory of Shock Waves by T.-P. Liu


Summary

In the field known as the mathematical theory of shock waves, very exciting and unexpected developments have occurred in the last few years. The stability theory of viscous shock waves has received a new, geometric perspective due to the work of Kevin Zumbrun and collaborators, which offers a spectral approach to systems.

Advances in the Theory of Shock Waves Summary

Advances in the Theory of Shock Waves by T.-P. Liu

In the field known as the mathematical theory of shock waves, very exciting and unexpected developments have occurred in the last few years. Joel Smoller and Blake Temple have established classes of shock wave solutions to the Einstein Euler equations of general relativity; indeed, the mathematical and physical con sequences of these examples constitute a whole new area of research. The stability theory of viscous shock waves has received a new, geometric perspective due to the work of Kevin Zumbrun and collaborators, which offers a spectral approach to systems. Due to the intersection of point and essential spectrum, such an ap proach had for a long time seemed out of reach. The stability problem for in viscid shock waves has been given a novel, clear and concise treatment by Guy Metivier and coworkers through the use of paradifferential calculus. The L 1 semi group theory for systems of conservation laws, itself still a recent development, has been considerably condensed by the introduction of new distance functionals through Tai-Ping Liu and collaborators; these functionals compare solutions to different data by direct reference to their wave structure. The fundamental prop erties of systems with relaxation have found a systematic description through the papers of Wen-An Yong; for shock waves, this means a first general theorem on the existence of corresponding profiles. The five articles of this book reflect the above developments.

Table of Contents

Preface * 'Well-Posedness Theory for a System of Hyperbolic Conservation Laws' / T.-P. LIU * 'Stability of Multidimensional Shocks' / G. METIVIER * 'Shock Wave Solutions of the Einstein Equations: A General Theory with Examples' / J. SMOLLER and B. TEMPLE * 'Basic Aspects of Hyperbolic Relaxation Systems' / W.-A. YONG * 'Multidimensional Stability of Planar Viscous Shock Waves' / K. ZUMBRUN

Additional information

NLS9781461266556
9781461266556
1461266556
Advances in the Theory of Shock Waves by T.-P. Liu
New
Paperback
Springer-Verlag New York Inc.
2012-10-24
520
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
This is a new book - be the first to read this copy. With untouched pages and a perfect binding, your brand new copy is ready to be opened for the first time

Customer Reviews - Advances in the Theory of Shock Waves