Flows of Non-Smooth Vector Fields and Degenerate Elliptic Equations

With Applications to the Vlasov-Poisson and Semigeostrophic Systems

Maria Colombo (Autor)

Buch | Softcover

250 Seiten

2017 | 2017 ed.
Scuola Normale Superiore (Verlag)
978-88-7642-606-3 (ISBN)

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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.

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.

Erscheinungsdatum	04.06.2017
Reihe/Serie	Publications of the Scuola Normale Superiore ; 22
Reihe/Serie	Theses (Scuola Normale Superiore)
Zusatzinfo	Approx. 250 p.
Verlagsort	Pisa
Sprache	englisch
Maße	150 x 240 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik
	Naturwissenschaften ► Biologie ► Ökologie / Naturschutz
	Naturwissenschaften ► Geowissenschaften ► Geophysik
Schlagworte	degenerate elliptic equation • Lagrangian flows • Optimal Transportation • renormalized solutions • semigeostrophic equations • traffic model • transport equations • Vlasov-Poisson system
ISBN-10	88-7642-606-X / 887642606X
ISBN-13	978-88-7642-606-3 / 9788876426063
Zustand	Neuware