Nonlinear Partial Differential Equations and Hyperbolic Wave Phenomena.

Intro -- Contents -- Preface -- A hyperbolic model of granular flow -- 1. The model of granular flow -- 2. Global smooth solutions -- 3. Global existence of large BV solutions -- 4. Global BV solutions of an initial boundary value problem -- 5. Slow erosion limit -- References -- Hilbertian approaches to some non-linear conservation laws -- On the asymptotic behavior of the gradient flow of a polyconvex functional -- On degenerate partial differential equations -- Symmetric solutions to multi-dimensional conservation laws -- Product estimates for wave-Sobolev spaces in 2 + 1 and 1 + 1 dimensions -- 1. Introduction -- 2. Notation and preliminaries -- 3. The case b0 = b1 = 0 &lt -- b2 -- 4. The case b0 = 0 &lt -- b1, b2 in 2d -- 5. The case 0 &lt -- b0, b1, b2 in 2d -- 6. The case b0 &lt -- 0 &lt -- b1, b2 in 2d -- 7. The product law in 1d -- References -- On the Cauchy problem for the modified Korteweg-de Vries equation with steplike finite-gap initial data -- Asymptotic analysis in thermodynamics of viscous fluids -- 1. Introduction -- 2. Mathematical theory of fluid dynamics -- 3. Long-time behavior -- 4. Scale analysis -- References -- Well-posedness and blow-up phenomena for a modified two-component Camassa-Holm equation -- Instability of solitary waves for a nonlinearly dispersive equation -- Kinetic relations for undercompressive shock waves. Physical, mathematical,and numerical issues -- Global regularity, and wave breaking phenomena in a class of nonlocaldispersive equations -- Potential based, constraint preserving, genuinely multi-dimensional schemes for systems of conservation laws -- A local and low-order Navier-Stokes-Korteweg system -- Local existence for viscous system of conservation laws: Hs-data with s &gt -- 1 + d/2 -- Finite difference methods for discretizing singular source terms in a Poisson interface problem.

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.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.