The topic of the 2010 Abel Symposium, hosted at the Norwegian Academy of Science and Letters, Oslo, was Nonlinear Partial Differential Equations, the study of which is of fundamental importance in mathematics and in almost all of natural sciences, economics, and engineering.
This area of mathematics is currently in the midst of an unprecedented development worldwide. Differential equations are used to model phenomena of increasing complexity, and in areas that have traditionally been outside the realm of mathematics. New analytical tools and numerical methods are dramatically improving our understanding of nonlinear models. Nonlinearity gives rise to novel effects reflected in the appearance of shock waves, turbulence, material defects, etc., and offers challenging mathematical problems. On the other hand, new mathematical developments provide new insight in many applications.
These proceedings present a selection of the latest exciting results by world leading researchers.
Author(s): Luigi Ambrosio (auth.), Helge Holden, Kenneth H. Karlsen (eds.)
Series: Abel Symposia 7
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2012
Language: English
Pages: 360
Tags: Partial Differential Equations;Mathematical Methods in Physics
Front Matter....Pages I-XVI
Convergence of Wigner Transforms in a Semiclassical Limit....Pages 1-11
Contractive Metrics for Nonsmooth Evolutions....Pages 13-35
Non-local Diffusions, Drifts and Games....Pages 37-52
Characteristic Discontinuities and Free Boundary Problems for Hyperbolic Conservation Laws....Pages 53-81
h -Principle and Rigidity for C 1,α Isometric Embeddings....Pages 83-116
About Existence, Symmetry and Symmetry Breaking for Extremal Functions of Some Interpolation Functional Inequalities....Pages 117-130
On the Oberbeck–Boussinesq Approximation on Unbounded Domains....Pages 131-168
Universal Profiles and Rigidity Theorems for the Energy Critical Wave Equation....Pages 169-174
A Simple Energy Pump for the Surface Quasi-geostrophic Equation....Pages 175-179
On the Formation of Trapped Surfaces....Pages 181-206
Surface Relaxation Below the Roughening Temperature: Some Recent Progress and Open Questions....Pages 207-221
Climate Science, Waves and PDEs for the Tropics....Pages 223-230
On the Propagation of Oceanic Waves Driven by a Strong Macroscopic Flow....Pages 231-254
Hierarchical Construction of Bounded Solutions of div U = F in Critical Regularity Spaces....Pages 255-269
Nonlinear Diffusion with Fractional Laplacian Operators....Pages 271-298
(Ir)reversibility and Entropy....Pages 299-360
