Flows of Non-Smooth Vector Fields and Degenerate Elliptic Equations: With Applications to the Vlasov-Poisson and Semigeostrophic Systems
Author:   Maria Colombo
Publisher:   Birkhauser Verlag AG
Edition:   2017 ed.
Volume:   22
ISBN:  

9788876426063


Pages:   250
Publication Date:   16 May 2017
Format:   Paperback
Availability:   In Print   Availability explained
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Flows of Non-Smooth Vector Fields and Degenerate Elliptic Equations: With Applications to the Vlasov-Poisson and Semigeostrophic Systems


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Overview

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.​

Full Product Details

Author:   Maria Colombo
Publisher:   Birkhauser Verlag AG
Imprint:   Scuola Normale Superiore
Edition:   2017 ed.
Volume:   22
ISBN:  

9788876426063


ISBN 10:   887642606
Pages:   250
Publication Date:   16 May 2017
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print   Availability explained
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.

Table of Contents

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. 

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