Displaying similar documents to “Painlevé analysis and similarity reductions for the magma equation.”

Wave fronts of solutions of some classes of non-linear partial differential equations

P. Popivanov (1992)

Banach Center Publications

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1. This paper is devoted to the study of wave fronts of solutions of first order symmetric systems of non-linear partial differential equations. A short communication was published in [4]. The microlocal point of view enables us to obtain more precise information concerning the smoothness of solutions of symmetric hyperbolic systems. Our main result is a generalization to the non-linear case of Theorem 1.1 of Ivriĭ [3]. The machinery of paradifferential operators introduced by Bony [1]...

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.

On global solutions to a nonlinear Alfvén wave equation

XS. Feng, F. Wei (1995)

Annales Polonici Mathematici

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We establish the global existence and uniqueness of smooth solutions to a nonlinear Alfvén wave equation arising in a finite-beta plasma. In addition, the spatial asymptotic behavior of the solution is discussed.