Advances in the Theory of Shock Waves (eBook)

Heinrich Freistuhler, Anders Szepessy (Herausgeber)

eBook Download: PDF

2012
Birkhauser Boston (Verlag)
978-1-4612-0193-9 (ISBN)

Infos

In the field known as "e;the mathematical theory of shock waves,"e; 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 "e;viscous"e; 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 "e;in- viscid"e; 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.

Produkt-Details

• Erscheint lt. Verlag: 6.12.2012
• Co-Autor: T.-P. Liu, G. Metivier, J. Smoller, B. Temple, W.-A. Yong, K. Zumbrun
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Naturwissenschaften ► Geowissenschaften ► Geophysik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• ISBN-10: 1-4612-0193-4 / 1461201934
• ISBN-13: 978-1-4612-0193-9 / 9781461201939