Nonlinear Partial Differential Equations and Hyperbolic Wave Phenomena
About this Title
Helge Holden and Kenneth H. Karlsen, Editors
This volume presents the state of the art in several directions of research conducted by renowned mathematicians who participated in the research program on Nonlinear Partial Differential Equations at the Centre for Advanced Study at the Norwegian Academy of Science and Letters, Oslo, Norway, during the academic year 2008–09.
The main theme of the volume is nonlinear partial differential equations that model a wide variety of wave phenomena. Topics discussed include systems of conservation laws, compressible Navier-Stokes equations, Navier-Stokes-Korteweg type systems in models for phase transitions, nonlinear evolution equations, degenerate/mixed type equations in fluid mechanics and differential geometry, nonlinear dispersive wave equations (Korteweg-de Vries, Camassa-Holm type, etc.), and Poisson interface problems and level set formulations.
Graduate students and research mathematicians interested in partial differental equations and nonlinear analysis.
Table of Contents
- Debora Amadori and Wen Shen – A hyperbolic model of granular flow [MR 2731985]
- Yann Brenier – Hilbertian approaches to some non-linear conservation laws [MR 2731986]
- José Antonio Carrillo and Stefano Lisini – On the asymptotic behavior of the gradient flow of a polyconvex functional [MR 2731987]
- Gui-Qiang G. Chen – On degenerate partial differential equations [MR 2731988]
- Nicola Costanzino and Helge Kristian Jenssen – Symmetric solutions to multi-dimensional conservation laws [MR 2731989]
- Piero D’Ancona, Damiano Foschi and Sigmund Selberg – Product estimates for wave-Sobolev spaces in $2+1$ and $1+1$ dimensions [MR 2731990]
- Iryna Egorova and Gerald Teschl – On the Cauchy problem for the modified Korteweg-de Vries equation with steplike finite-gap initial data [MR 2731991]
- Eduard Feireisl – Asymptotic analysis in thermodynamics of viscous fluids [MR 2731992]
- Chunxia Guan, Kenneth H. Karlsen and Zhaoyang Yin – Well-posedness and blow-up phenomena for a modified two-component Camassa-Holm equation [MR 2731993]
- Henrik Kalisch and Nguyet Thanh Nguyen – Instability of solitary waves for a nonlinearity dispersive equation [MR 2731994]
- Philippe G. LeFloch – Kinetic relations for undercompressive shock waves. Physical, mathematical, and numerical issues [MR 2731995]
- Hailiang Liu and Zhaoyang Yin – Global regularity, and wave breaking phenomena in a class of nonlocal dispersive equations [MR 2731996]
- Siddhartha Mishra and Eitan Tadmor – Potential based, constraint preserving, genuinely multi-dimensional schemes for systems of conservation laws [MR 2731997]
- Christian Rohde – A local and low-order Navier-Stokes-Korteweg system [MR 2731998]
- Denis Serre – Local existence for viscous system of conservation laws: $H^s$-data with $s>1+d/2$ [MR 2731999]
- John D. Towers – Finite difference methods for discretizing singular source terms in a Poisson interface problem [MR 2732000]