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＜電子ブック＞
Flows of Non-Smooth Vector Fields and Degenerate Elliptic Equations : With Applications to the Vlasov-Poisson and Semigeostrophic Systems / by Maria Colombo
(Theses. ISSN:25321668 ; 22)

版	1st ed. 2017.
出版者	(Pisa : Scuola Normale Superiore : Imprint: Edizioni della Normale)
出版年	2017
本文言語	英語
大きさ	Approx. 250 p : online resource
著者標目	*Colombo, Maria author SpringerLink (Online service)
件　名	LCSH:Differential equations LCSH:Mathematical optimization LCSH:Calculus of variations LCSH:Environmental sciences LCSH:Physics FREE:Differential Equations FREE:Calculus of Variations and Optimization FREE:Environmental Physics
一般注記	An overview on flows of vector fields and on optimal transport -- Maximal regular flows for non-smooth vector fields -- Main properties of maximal regular flows and analysis of blow-up -- Lagrangian structure of transport equations -- The continuity equation with an integrable damping term -- Regularity results for very degenerate elliptic equations -- An excess-decay result for a class of degenerate elliptic equations -- The Vlasov-Poisson system -- The semigeostrophic system. The first part of the book is devoted to the transport equation for a given vector field, exploiting the lagrangian structure of solutions. It also treats the regularity of solutions of some degenerate elliptic equations, which appear in the eulerian counterpart of some transport models with congestion. The second part of the book deals with the lagrangian structure of solutions of the Vlasov-Poisson system, which describes the evolution of a system of particles under the self-induced gravitational/electrostatic field, and the existence of solutions of the semigeostrophic system, used in meteorology to describe the motion of large-scale oceanic/atmospheric flows HTTP:URL=https://doi.org/10.1007/978-88-7642-607-0

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