Painlevé analysis and similarity reductions for the magma equation.
Harris, Shirley E., Clarkson, Peter A. (2006)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Harris, Shirley E., Clarkson, Peter A. (2006)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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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.
Mihai Mariş (2010)
Journées Équations aux dérivées partielles
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This text is a survey of recent results on traveling waves for nonlinear Schrödinger equations with nonzero conditions at infinity. We present the existence, nonexistence and stability results and we describe the main ideas used in proofs.
Gama, Silvio Marques A., Smirnov, Gueorgui (2009)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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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]...
Gorman, Arthur D., Yang, Huijun (2001)
International Journal of Mathematics and Mathematical Sciences
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Boni, Theodore K., Nabongo, Diabate, Sery, Roger B. (2008)
The Journal of Nonlinear Sciences and its Applications
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Nader Masmoudi (2003)
Journées équations aux dérivées partielles
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Existence of solutions to many kinds of PDEs can be proved by using a fixed point argument or an iterative argument in some Banach space. This usually yields uniqueness in the same Banach space where the fixed point is performed. We give here two methods to prove uniqueness in a more natural class. The first one is based on proving some estimates in a less regular space. The second one is based on a duality argument. In this paper, we present some results obtained in collaboration with...
Jones, Kenneth L. (2000)
International Journal of Mathematics and Mathematical Sciences
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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.