TY - BOOK ID - 67107802 TI - Geometric analysis of hyperbolic differential equations : an introduction PY - 2010 VL - 374 SN - 9780521128223 9781139127844 1139127845 9781139107198 1139107194 9781139115018 1139115014 0521128226 1107203589 9781107203587 1283296039 9781283296038 1139122924 9781139122924 9786613296030 6613296031 1139117181 9781139117180 1139112821 9781139112826 PB - Cambridge: Cambridge university press, DB - UniCat KW - Nonlinear wave equations. KW - Differential equations, Hyperbolic. KW - Quantum theory. KW - Geometry, Differential. KW - Differential geometry KW - Quantum dynamics KW - Quantum mechanics KW - Quantum physics KW - Physics KW - Mechanics KW - Thermodynamics KW - Hyperbolic differential equations KW - Differential equations, Partial KW - Wave equation UR - https://www.unicat.be/uniCat?func=search&query=sysid:67107802 AB - "The field of nonlinear hyperbolic equations or systems has seen a tremendous development since the beginning of the 1980s. We are concentrating here on multidimensional situations, and on quasilinear equations or systems, that is, when the coefficients of the principal part depend on the unknown function itself. The pioneering works by F. John, D. Christodoulou, L. Hormander, S. Klainerman, A. Majda and many others have been devoted mainly to the questions of blowup, lifespan, shocks, global existence, etc. Some overview of the classical results can be found in the books of Majda [42] and Hormander [24]. On the other hand, Christodoulou and Klainerman [18] proved in around 1990 the stability of Minkowski space, a striking mathematical result about the Cauchy problem for the Einstein equations. After that, many works have dealt with diagonal systems of quasilinear wave equations, since this is what Einstein equations reduce to when written in the so-called harmonic coordinates. The main feature of this particular case is that the (scalar) principal part of the system is a wave operator associated to a unique Lorentzian metric on the underlying space-time"--Provided by publisher. ER -