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Next: 2.4. Numerical Analysis Up: Analysis Previous: 2.2. Lie Theory and

2.3. Non-linear Differential Equations

Programme leaders: L.A. Peletier, S.M. Verduyn Lunel

This project focusses on the mathematical analysis of nonlinear ordinary and partial differential equations, frequently suggested by problems in mathematical physics and engineering (e.g. the Swift-Hohenberg equation, the Ginzburg-Landau equation, the Navier Stokes equations, the Porous Media equation, or the Korteweg de Vries equation). Typical questions concern: the existence of solutions, uniqueness and multiplicity properties, regularity, qualitative behaviour, and asymptotic properties of solutions.

New results were obtained for the set of periodic solutions of the Swift-Hohenberg equation and the Extended Fisher-Kolmogorov equation. The underlying nonlinear eigenvalue problem has become much better understood, and the existence of global branches of periodic solutions with increasing complexity has been established.