Besides a general background in mathematical analysis, the course has no firm prerequisites. Any necessary tools from neighboring fields are introduced during the lecture, depending on the audience. That said, it will be very helpful if you have at least a basic familiarity with the following topics:
- matrix exponential
- stability of fixed point for ODEs
- phase portrait analysis
- Hilbert spaces
- basic Fourier analysis
Aim of the course
Waves play an important role in various applications and are an essential topic in modern applied mathematics.
This is an introductory course on the analysis of traveling waves and several other special solutions to nonlinear partial differential equations (PDEs).
Its core theme is the examination of their existence and stability, which can be carried out through a blend of techniques from dynamical systems theory, functional analysis, spectral theory and ordinary differential equations.
Rules about Homework / Exam
Graded homework will account for 40% of the final grade. The final exam yields the remaining 60%.
Lecture Notes / Literature
Todd Kapitula and Keith Promislow: Spectral and Dynamical Stability of Nonlinear Waves ISBN 978-1-4614-6994-0 or ISBN 978-1-4614-6995-7 (eBook)
Some universities allow you to download a pdf of this book directly from Springer