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Some partial differential equations in Clifford analysis

Elena Obolashvili (1996)

Banach Center Publications

Using Clifford analysis in a multidimensional space some elliptic, hyperbolic and parabolic systems of partial differential equations are constructed, which are related to the well-known classical equations. To obtain parabolic systems Clifford algebra is modified and some corresponding differential operator is constructed. For systems obtained the boundary and initial value problems are solved.

Some remarks on the continuity equation

Patrick Bernard (2008/2009)

Séminaire Équations aux dérivées partielles

This text is the act of a talk given november 18 2008 at the seminar PDE of Ecole Polytechnique. The text is not completely faithfull to the oral exposition for I have taken this opportunity to present the proofs of some results that are not easy to find in the literature. On the other hand, I have been less precise on the material for which I found good references. Most of the novelties presented here come from a joined work with Luigi Ambrosio.

Systèmes hyperboliques et viscosité évanescente

Frédéric Rousset (2002/2003)

Séminaire Bourbaki

Le but de l’exposé est de présenter les résultats obtenus par S. Bianchini et A. Bressan sur le problème de Cauchy pour des perturbations visqueuses t u ε + x f ( u ε ) = ε x x u ε de systèmes strictement hyperboliques t u + x f ( u ) = 0 en une dimension d’espace. Ils ont en particulier montré l’existence globale ( t 0 ), l’unicité et la stabilité des solutions et justifié la convergence quand ε tend vers zéro pour des données initiales à petite variation totale. Leur analyse montre aussi que les solutions du système hyperbolique ainsi obtenues...

Systems of Clairaut type

Shyuichi Izumiya (1993)

Colloquium Mathematicae

A characterization of systems of first order differential equations with (classical) complete solutions is given. Systems with (classical) complete solutions that consist of hyperplanes are also characterized.

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