Bifurcation theory for dissipative systems on unbounded cylindrical domains - An introduction to the mathematical theory of modulation equations

摘要

In this introductory text we consider dissipative translational invariant nonlinear partial differential equations on spatially unbounded cylindrical domains close to the threshold of instability. We give an overview about the mathematical theory of modulation equations which allows us to analyse bifurcation problems occurring in such systems. We explain this theory by presenting new results concerning the dynamics of interface solutions bifurcating in certain reaction-diffusion systems. [References: 64]