Existence of global solution of a nonlinear wave equation with short-range potential
V. Georgiev, K. Ianakiev (1992)
Banach Center Publications
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V. Georgiev, K. Ianakiev (1992)
Banach Center Publications
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Fonseca, Germán E. (2000)
Revista Colombiana de Matemáticas
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Christopher Sogge (1997)
Banach Center Publications
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Hart F. Smith (2001)
Journées équations aux dérivées partielles
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This talk describes joint work with Chris Sogge and Markus Keel, in which we establish a global existence theorem for null-type quasilinear wave equations in three space dimensions, where we impose Dirichlet conditions on a smooth, compact star-shaped obstacle . The key tool, following Christodoulou [1], is to use the Penrose compactification of Minkowski space. In the case under consideration, this reduces matters to a local existence theorem for a singular obstacle problem. Full details...
Vaidya, A., Sparling, A.J. (2003)
Acta Mathematica Universitatis Comenianae. New Series
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Serge Alinhac (2002)
Journées équations aux dérivées partielles
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The aim of this mini-course is twofold: describe quickly the framework of quasilinear wave equation with small data; and give a detailed sketch of the proofs of the blowup theorems in this framework. The first chapter introduces the main tools and concepts, and presents the main results as solutions of natural conjectures. The second chapter gives a self-contained account of geometric blowup and of its applications to present problem.
Jeffrey Rauch (2001)
Journées équations aux dérivées partielles
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This talk gives a brief review of some recent progress in the asymptotic analysis of short pulse solutions of nonlinear hyperbolic partial differential equations. This includes descriptions on the scales of geometric optics and diffractive geometric optics, and also studies of special situations where pulses passing through focal points can be analysed.
Pierre Germain (2010)
Journées Équations aux dérivées partielles
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This article is a short exposition of the space-time resonances method. It was introduced by Masmoudi, Shatah, and the author, in order to understand global existence for nonlinear dispersive equations, set in the whole space, and with small data. The idea is to combine the classical concept of resonances, with the feature of dispersive equations: wave packets propagate at a group velocity which depends on their frequency localization. The analytical method which follows from this idea...
Karoline Johansson, Stevan Pilipović, Nenad Teofanov, Joachim Toft (2012)
Publications de l'Institut Mathématique
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