Displaying similar documents to “Existence of global solution of a nonlinear wave equation with short-range potential”

Global existence for a quasilinear wave equation outside of star-shaped domains

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 𝒦 ⊂ ℝ 3 . 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...

A minicourse on global existence and blowup of classical solutions to multidimensional quasilinear wave equations

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.