This volume contains research and expository articles from the research pro-
gram on Nonlinear Partial Differential Equations at the Centre for Advanced Study
at the Norwegian Academy of Science and Letters in Oslo, Norway during the aca-
demic year 2008–09. The program was one of three programs hosted at the Centre
for Advanced Study during 2008–09; in addition there was one program in social
sciences and one in humanities, thereby creating a unique atmosphere for cross
disciplinary discussions. Within the program on nonlinear partial differential equa-
tions 40 researchers from all over the world participated. Our program focused on
nonlinear partial differential equations modeling various wave phenomena. There
was a certain emphasis on nonlinear hyperbolic waves which is reflected in the cur-
rent volume.
Each one of the articles in this volume represents current advances in the area of
nonlinear partial differential equations. A range of topics is covered, including sys-
tems of conservation laws, Navier–Stokes equations of compressible viscous fluids,
Navier–Stokes–Korteweg type systems and models for phase transitions, nonlin-
ear evolution equations, degenerate/mixed type nonlinear partial differential equa-
tions arising in fluid mechanics and differential geometry, nonlinear dispersive wave
equations (Korteweg–de Vries, Camassa–Holm, etc.), and Poisson interface prob-
lems and level set formulations. The articles reflect recent developments in nonlin-
ear analysis, and touch upon many methods from functional analysis and calculus
of variations, including entropy analysis, renormalization, weak convergence tech-
niques, kinetic formulations, non-classical shocks and kinetic relations, asymptotic
analysis, gradient flows, and numerical methods. The volume is suitable for gradu-
ate students and researchers interested in nonlinear analysis and partial differential
Our research was generously funded by the Centre for Advanced Study, and all
our activities at the Centre were greatly facilitated by the very able and friendly
staff at the Centre, namely Willy Østreng, Trude Gran Peters, Maria Sætre, and
Marit Finnemyhr Strøm.
Trondheim and Oslo, June 3, 2010
Helge Holden and Kenneth H. Karlsen
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