Partial differential equations are a fundamental tool in science and engineering. In fact, many of the laws of physics can be formulated in terms of such equations. In addition, they are of great importance in other areas of mathematics such as differential geometry. Lund has a strong tradition of research in partial differential equations. Today the following areas are represented:
- Microlocal analysis and pseudodifferential operators.
- Pseudospectra of non-selfadjoint operators.
- Nonlinear waves and fluid mechanics.
- Spectral theory for magnetic Schrödinger operators and Ginzburg-Landau theory.
The figure illustrates pseudospectra of the anharmonic oscillator -u''+(1+3i)x^2u. In contrast to selfadjoint operators, it has large resolvent norm far away from the spectrum. The picture is taken from the Pseudospectra Gateway http://www.cs.ox.ac.uk/pseudospectra/