Project name: PDEs at CWI - MAS1.2 (PDE@CWI)

Of research group: Dynamical Systems and Numerical Analysis

Coordinator of this project: Mark Peletier
Startdate: 2002-10-01
Enddate: 2004-12-31

This subtheme collects the actitivities of the Professors Doelman, Van Duijn, Hulshof, and L. A. Peletier. The goal of this subtheme is to generate research activity in the analysis of PDEs by creating a `hot spot' of PDE-analysis at the CWI.
See the PDE@CWI webpage.

Description of projects

• MAS 1.2 - PDEBOOK
  Symmetry properties of solutions of partial differential equations often translate into special, symmetric solutions such as self-similar solutions, travelling waves and radially symmetric solutions, which play a key role in applications. They are often solutions of ordinary differential equations with a special structure.
  The literature on such equations is ubiquitous but scattered over the mathematical, engineering, and physics literature. C.J. van Duijn and L.A. Peletier are writing a textbook aimed at graduate students in mathematics, physics and engineering, offering a systematic introduction to these equations and the properties of their solutions.
• MAS 1.2 - GS
  In 1983 Gray and Scott proposed a system of two reaction-diffusion equations as a model system for understanding complex dynamics in chemical reactions, and the understanding of the formation of patterns such as the birth of multi-bump spikes and travelling fronts. This system leads to nonlinear eigenvalue problems with several eigenvalues, involving a variety of (repeated) bifurcations. In a joint project A. Doelman, L.A. Peletier and T.J. Kaper from Boston University are studying a sequence of saddle-node bifurcations leading to a hierarchy of spikes with increasing complexity.
• MAS 1.2 - LFBP
  Free boundary problems (FBP's) for partial differential equations (PDE's) appear in many applications in the exact sciences. The classical example is the Stefan problem for water-ice. Other applications involve cell boundaries, contact lines in thin film flows, and flame fronts in combustion models.
  FBP's may appear as limits of (systems of) reaction-diffusion equations (RDE's) which have been studied extensively from a dynamical systems viewpoint. In this project we aim at a theory for FBP's which parallels that of RDE's: linearisation, Evans functions, rigorous nonlinear stability and bifurcation analysis, etc. A main application is the thermo-diffusive model for combustion in dusty, gaseous mixtures, where the presence of dust accounts for nonlocal terms in the temperature equation. These are due to radiative effects which have a strong effect on flame temperatures and speeds.

Members
Arjen Doelman, Hans van Duijn, Joost Hulshof, Bert Peletier, Mark Peletier.