Nonlinear Differential Equation Models

The papers in this book originate from lectures which were held at the "Vienna Workshop on Nonlinear Models and Analysis" - May 20-24, 2002.They represent a cross-section of the research field Applied Nonlinear Analysis with emphasis on free boundaries, fully nonlinear partial differential equations, variational methods, quasilinear partial differential equations and nonlinear kinetic models.

On the Curvature of the Free Boundary for the Obstacle Problem in Two Dimensions (B. Gustafsson, M. Sakai) Nonlinear Free Boundary Problems with Singular Source Terms (A. Hakobyan, A. Karakhanyan) Behavior of the Free Boundary Near Contact Points with the Fixed Boundary for Nonlinear Elliptic Equations (N. Matevosyan, P. A. Markowich) Global Solutions of an Obstacle-Problem-Like Equation With Two Phases (H. Shahgholian, N. Uraltseva, G. S. Weiss) Entropies and Equilibria of Many-Particle Systems: An Essay on Recent Research (A. Arnold, J. A. Carrillo, L. Desvillettes, J. Dolbeault, A. Jüngel, C. Lederman, P. A. Markowich, G. Toscani, C. Villani) On the Blow-Up Set for ut = (um)xx, m > 1, with Nonlinear Boundary Conditions (M. C. Cortázar, M. Elgueta, O. Venegas) A Phase Plane Analysis of the 'Multi-Bubbling" Phenomenon in Some Slightly Supercritical Equations (M. del Pino, J. Dolbeault, M. Musso) The Dirichlet Problem for the Porous Medium Equation in Bounded Domains. Asymptotic Behavior (J. L. Vazquez) A Note on Deformations of 2D Fluid Motions Using 3D Born-Infeld Equations (Y. Brenier) Kinetic Models for Chemotaxis and their Drift-Diffusion Limits (F. A. C. C. Chalub, P. A. Markowich, B. Perthame, C. Schmeiser) Rotating Charge Coupled to the Maxwell Field: Scattering Theory and Adiabatic Limit (V. Imaikin, A. Komech, H. Spohn) On Hyperbolic Variational Inequalities of First Order and Some Applications (J. F. Rodrigues) Kinetic and Hydrodynamic Models of Nearly Elastic Granular Flows (G. Toscani)