Transport Equations and Multi-D Hyperbolic Conservation Laws / Edition 1

by Luigi Ambrosio, Fabio Ancona, Gianluca Crippa, Stefano Bianchini, Camillo De Lellis

Overview

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.

Product Details

ISBN-13:	9783540767800
Publisher:	Springer Berlin Heidelberg
Publication date:	03/11/2008
Series:	Lecture Notes of the Unione Matematica Italiana , #5
Edition description:	2008
Pages:	131
Product dimensions:	5.90(w) x 9.20(h) x 0.30(d)

Table of Contents

I.- Existence, Uniqueness, Stability and Differentiability Properties of the Flow Associated to Weakly Differentiable Vector Fields.- II.- A Note on Alberti's Rank-One Theorem.- III.- Regularizing Effect of Nonlinearity in Multidimensional Scalar Conservation Laws.