Handbook of Differential Equations: Evolutionary Equations: Evolutionary Equations
Author(s): Dafermos, C.M.; Pokorny, Milan
Publisher: North Holland
ISBN: 9780444532220
Edition:
$39,99
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The material collected in this volume discusses the present as well as expected future directions of development of the field with particular emphasis on applications. The seven survey articles present different topics in Evolutionary PDE’s, written by leading experts.
– Review of new results in the area
– Continuation of previous volumes in the handbook series covering evolutionary PDEs
– New content coverage of DE applications
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Handbook of Differential Equations: Evolutionary Equations: Evolutionary Equations
Author(s): Dafermos, C.M.; Feireisl, Eduard
Publisher: North Holland
ISBN: 9780444528483
Edition:
$39,99
Delivery: This can be downloaded Immediately after purchasing.
Version: Only PDF Version.
Compatible Devices: Can be read on any device (Kindle, NOOK, Android/IOS devices, Windows, MAC)
Quality: High Quality. No missing contents. Printable
Recommended Software: Check here
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Description
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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-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
Related products
Handbook of Differential Equations: Evolutionary Equations: Evolutionary Equations
Author(s): Dafermos, C.M.; Feireisl, Eduard
Publisher: North Holland
ISBN: 9780444520487
Edition:
$39,99
Delivery: This can be downloaded Immediately after purchasing.
Version: Only PDF Version.
Compatible Devices: Can be read on any device (Kindle, NOOK, Android/IOS devices, Windows, MAC)
Quality: High Quality. No missing contents. Printable
Recommended Software: Check here
Important: No Access Code
Description
Description
The aim of this Handbook is to acquaint the reader with the current status of the theory of evolutionary partial differential equations, and with some of its applications. Evolutionary partial differential equations made their first appearance in the 18th century, in the endeavor to understand the motion of fluids and other continuous media. The active research effort over the span of two centuries, combined with the wide variety of physical phenomena that had to be explained, has resulted in an enormous body of literature. Any attempt to produce a comprehensive survey would be futile. The aim here is to collect review articles, written by leading experts, which will highlight the present and expected future directions of development of the field. The emphasis will be on nonlinear equations, which pose the most challenging problems today.
. Volume I of this Handbook does focus on the abstract theory of evolutionary equations.
. Volume 2 considers more concrete problems relating to specific applications.
. Together they provide a panorama of this amazingly complex and rapidly developing branch of mathematics.
