Transport equations and multi-d hyperbolic conservation laws

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 twoareas of research in PDEs, related to hyperbolic conservation laws. Geometricand 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 solutionsto multi-dimensional scalar conservation laws. The volume contains surveys ofrecent deep results, provides an overview of further developments and relatedopen problems, and will capture the interest of members both of the hyperbolic and the elliptic community willing to explore the intriguing interplays thatlink their worlds. Readers should have basic knowledge of PDE and measure theory. INDICE: Preface. Part I by L. Ambrosio and G. Crippa: Existence, uniqueness, stability and differentiability properties of the flow associated to weaklydifferentiable 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.

• ISBN: 978-3-540-76780-0
• Editorial: Springer
• Encuadernacion: Rústica
• Páginas: 230
• Fecha Publicación: 01/02/2008
• Nº Volúmenes: 1
• Idioma: Inglés