
Handbook of Differential Equations: Evolutionary Equations: Volume 3
Volume 3
North-Holland (Publisher)
Published on 24. October 2006
Book
Hardback
652 pages
978-0-444-52848-3 (ISBN)
Description
The material collected in this volume reflects the active present of this area of mathematics, ranging from the abstract theory of gradient flows to stochastic representations of non-linear parabolic PDE's.Articles will highlight the present as well as expected future directions of development of the field with particular emphasis on applications. The article by Ambrosio and Savare discussesthe most recent development in the theory of gradient flow of probability measures. After an introduction reviewing the properties of the Wasserstein space and corresponding subdifferential calculus, applications are given to evolutionarypartial differential equations. The contribution of Herrero provides a description of some mathematical approaches developed to account for quantitative as well as qualitative aspects of chemotaxis. Particular attention is paid to the limits of cell'scapability to measure external cues on the one hand, and to provide an overall description of aggregation models for the slim mold Dictyostelium discoideum on the other.The chapter written by Masmoudi deals with a rather different topic - examples of singular limits in hydrodynamics. This is nowadays a well-studied issue given the amount of new results based on the development of the existence theory for rather general systems of equations in hydrodynamics. The paper by DeLellis addreses the most recent results for the transport equations with regard to possible applications in the theory of hyperbolic systems of conservation laws. Emphasis is put on the development of the theory in the case when the governing field is only a BV function.The chapter by Rein represents a comprehensive survey of results on the Poisson-Vlasov system in astrophysics. The question of global stability of steady states is addressed in detail. The contribution of Soner is devoted to different representations of non-linear parabolic equations in terms of Markov processes. After a brief introduction on the linear theory, a class ofnon-linear equations is investigated, with applications to stochastic control and differential games.The chapter written by Zuazua presents some of the recent progresses done on the problem of controllabilty of partial differential equations. The applications include the linear wave and heat equations,parabolic equations with coefficients of low regularity, and some fluid-structure interaction models.
More details
Series
Language
English
Place of publication
United States
Publishing group
Elsevier Science & Technology
Target group
Professional and scholarly
University libraries and Research mathematicians
Product notice
sewn/stitched
Paper over boards
Dimensions
Height: 246 mm
Width: 172 mm
Thickness: 30 mm
Weight
1315 gr
ISBN-13
978-0-444-52848-3 (9780444528483)
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Schweitzer Classification
Other editions
Additional editions

C. M. Dafermos | Eduard Feireisl
Handbook of Differential Equations: Evolutionary Equations
E-Book
09/2011
Elsevier
€200.00
Available for download
Persons
Editor
Brown University, Providence, RI, USA
Mathematical Institute AS CR, Prague, Czech Republic.
Content
Preface
Contributors
1.L. Ambriosio, G. Savare: Gradient flows of probability measures
2.M.A. Herrero: The mathematics of chemotaxis
3.N. Masmoudi: Examples of singular limits in hydrodynamics
4. C. DeLellis: Notes on hyperbolic systems of conservation laws and transport equations
5. G. Rein: Collisionless kinetic equations from astrophysics - the Vlasov-Poisson system
6. H.M. Stochastic representations for non-linear parabolic PDE's
7. E. Zuazua Controllability and observability of partial differential equations: Some results and open problems
Index
Contributors
1.L. Ambriosio, G. Savare: Gradient flows of probability measures
2.M.A. Herrero: The mathematics of chemotaxis
3.N. Masmoudi: Examples of singular limits in hydrodynamics
4. C. DeLellis: Notes on hyperbolic systems of conservation laws and transport equations
5. G. Rein: Collisionless kinetic equations from astrophysics - the Vlasov-Poisson system
6. H.M. Stochastic representations for non-linear parabolic PDE's
7. E. Zuazua Controllability and observability of partial differential equations: Some results and open problems
Index