Contact manifolds, Lagrangian Grassmannians and PDEs
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Abstract In this paper we review a geometric approach to PDEs. We mainly focus on scalar PDEs in n independent variables and one dependent variable of order one and two, by insisting on the underlying (2n + 1)-dimensional contact manifold and the so-called Lagrangian Grassmannian bundle over the latter. This work is based on a Ph.D course given by two of the authors (G. M. and G. M.). As such, it was mainly designed as a quick introduction to the subject for graduate students. But also the more demanding reader will be gratified, thanks to the frequent references to current research topics and glimpses of higher-level mathematics, found mostly in the last sections.
2017 ◽
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Status of Centrifugal Impeller Internal Aerodynamics—Part II: Experiments and Influence of Viscosity
1980 ◽
Vol 102
(3)
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pp. 738-746
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2018 ◽
Vol 29
(04)
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pp. 1850026
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