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Transport Equations and Multi-D Hyperbolic Conservation Laws
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Catalogue Information
Field name
Details
Dewey Class
515.353
Title
Transport Equations and Multi-D Hyperbolic Conservation Laws ([Ebook]) / by Luigi Ambrosio, Gianluca Crippa, Camillo Lellis, Felix Otto, Michael Westdickenberg.
Author
Ambrosio, Luigi. , 1963-
Added Personal Name
Crippa, Gianluca
Lellis, Camillo
Otto, Felix
Westdickenberg, Michael
Other name(s)
SpringerLink (Online service)
Publication
Berlin, Heidelberg : Springer , 2008.
Physical Details
: online resource.
Series
Lecture Notes of the Unione Matematica Italiana
1862-9113 ; ; 5
ISBN
9783540767817
Summary Note
The theory of nonlinear hyperbolic equations in several space dimensions has recently obtained remarkable achievements thanks to ideas and techniques related to the structure and fine properties of functions of bounded variation. This volume provides an up-to-date overview of the status and perspectives of two areas of research in PDEs, related to hyperbolic conservation laws. Geometric and measure theoretic tools play a key role to obtain some fundamental advances: the well-posedness theory of linear transport equations with irregular coefficients, and the study of the BV-like structure of bounded entropy solutions to multi-dimensional scalar conservation laws. The volume contains surveys of recent deep results, provides an overview of further developments and related open problems, and will capture the interest of members both of the hyperbolic and the elliptic community willing to explore the intriguing interplays that link their worlds. Readers should have basic knowledge of PDE and measure theory.:
Contents note
Preface -- Part I by L. Ambrosio and G. Crippa: Existence, uniqueness, stability and differentiability properties of the flow associated to weakly differentiable vector fields -- Part II by C. De Lellis: A note on Alberti's rank-one theorem -- Part III by G. Crippa, F. Otto and M. Westdickenberg: Regularizing effect of nonlinearity in multidimensional scalar conservation laws -- Index.
System details note
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site
http://dx.doi.org/10.1007/978-3-540-76781-7
Links to Related Works
Subject References:
Calculus of variations and optimal control; optimization
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Differential equation
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Differential equations, Partial
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Mathematical optimization
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Mathematics
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Measure and Integration
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Ordinary differential equations
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Partial differential equations
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Authors:
Ambrosio, Luigi. 1963-
.
author
.
Crippa, Gianluca
.
Lellis, Camillo
.
Otto, Felix
.
Westdickenberg, Michael
.
Corporate Authors:
SpringerLink (Online service)
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Series:
Lecture Notes of the Unione Matematica Italiana
.
Classification:
515.353
.
515.353 (DDC 23)
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