| Edition |
1st ed. |
| Description |
1 online resource : illustrations |
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text txt rdacontent |
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computer c rdamedia |
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online resource cr rdacarrier |
| Note |
Vol. 5 edited by C.M. Dafermos, Milan Pokorný. |
| Summary |
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 Sava 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-linear parabolic equations in terms of Markov processes. After a brief introduction on the linear theory, a class of non-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. - 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. |
| Bibliography |
Includes bibliographical references and indexes. |
| Contents |
Preface -- Contributors -- 1.L. Ambriosio, G. Sava: 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. |
| Note |
Print version record. |
| Access |
Use copy Restrictions unspecified star MiAaHDL |
| Reproduction |
Electronic reproduction. [Place of publication not identified] : HathiTrust Digital Library, 2010. MiAaHDL |
| System Details |
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL |
| Processing Action |
digitized 2010 HathiTrust Digital Library committed to preserve pda MiAaHDL |
| Subject |
Differential equations.
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Evolution equations.
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Differential equations, Partial.
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Differential equations -- Handbooks, manuals, etc.
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Équations différentielles -- Guides, manuels, etc.
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Équations différentielles.
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Équations d'évolution.
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Équations aux dérivées partielles.
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Differential equations
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Differential equations, Partial
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Evolution equations
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| Genre/Form |
handbooks.
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Handbooks and manuals
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Handbooks and manuals.
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Guides et manuels.
|
| Added Author |
Dafermos, C. M. (Constantine M.)
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Feireisl, Eduard.
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Pokorný, Milan.
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| Other Form: |
Print version: Handbook of differential equations. 1st ed. Amsterdam ; Boston : Elsevier/North Holland, 2004-2009 9780444517449 (DLC) 2005052581 (OCoLC)61228805 |
| ISBN |
9780080931975 (v. 4 ; ebook) |
|
0080931979 (v. 4 ; ebook) |
|
9780080932590 (v. 5 ; ebook) |
|
0080932592 (v. 5 ; ebook) |
|
128102144X |
|
9781281021441 |
|
1280638494 |
|
9781280638497 |
|
9780444517449 (set ; alk. paper) |
|
0444517448 (set ; alk. paper) |
|
0444511318 (v. 1 ; alk. paper) |
|
9780444511317 (v. 1 ; alk. paper) |
|
9780444520487 (v. 2 ; alk. paper) |
|
0444520481 (v. 2 ; alk. paper) |
|
0444528482 (v. 3) |
|
9780444528483 (v. 3) |
|
9780444530349 (v. 4) |
|
0444530347 (v. 4) |
|
9780444532220 (v. 5) |
|
0444532226 (v. 5) |
| Standard No. |
AU@ 000048130049 |
|
CHNEW 001006672 |
|
DEBBG BV036962198 |
|
DEBSZ 275200612 |
|
DEBSZ 434149330 |
|
DEBSZ 482356170 |
|
NZ1 11778559 |
|
NZ1 13084612 |
|
NZ1 15177283 |
|
