240161 Waves in Evolution Equations (V) (SoSe 2017)

Many transport phenomena in the natural sciences can be described in
mathematical terms as wave solutions of nonlinear evolution equations.
Examples of such phenomena are the transfer of neural signals,
the spread of epidemics and populations, the propagation of flame fronts in
combustion, surface waves of fluids, and spiral waves in chemically
excitable media.

The main topic of this lecture are qualitative properties and the
numerical computation of such waves in time-dependent partial differential
equations. To a lesser extent we will also investigate the existence and
uniquess of waves. Another major topic will be the spectral properties
and Lyapunov stability of the wave profiles.

Some experience with numerical methods and some basic knowledge
of ordinary and partial differential equations is assumed.

A monograph that shows the range of topics is

T. Kapitula, K. Promislow: Spectral and Dynamical Stability
of Nonlinear Waves, Springer 2013.

The lecture is also intended to initiate and support students of
Mathematics who want to write a Master Thesis in Applied or Numerical
Analysis.

Bibliography

T. Kapitula, K. Promislow: Spectral and Dynamical Stability
of Nonlinear Waves, Springer 2013.