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# Volume 3. Handbook of Differential Equations: Evolutionary Equations

## 1st Edition

Editors:

- eBook ISBN 9780080465654
- Print ISBN 9780444528483
- Print ISBN 9780444561374

Editors:

- eBook ISBN 9780080465654
- Print ISBN 9780444528483
- Print ISBN 9780444561374

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 Savaré discusses
the 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 evolutionary
partial 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's
capability 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-lin

- Volume 1 focuses on the abstract theory of evolution
- Volume 2 considers more concrete probelms relating to specific applications
- Volume 3 reflects the active present of this area of mathematics, ranging from the abstract theory of gradient flows to stochastic representations of non-linear PDEs

University libraries and Research mathematicians

Preface

Contributors

1.L. Ambriosio, G. Savaré: 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. Savaré: 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

- No. of pages:
- 652

- Language:
- English

- Copyright:
- © 2007

- Published:
- 24th October 2006

- Imprint:
- North Holland

- eBook ISBN:
- 9780080465654

- Print ISBN:
- 9780444528483

- Print ISBN:
- 9780444561374

Brown University, Providence, RI, USA

Mathematical Institute AS CR, Prague, Czech Republic.

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 Savaré discusses
the 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 evolutionary
partial 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's
capability 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-lin