Bifurcation theory for dissipative systems on unbounded cylindrical domains. -- An introduction to the mathematical theory of modulation equations (Q2746567)

In this introductory article the author considers dissipative translational invariant nonlinear partial differential equations posed on spatially unbounded cylindrical domains close to the threshold of instability. Comparing the system with the case of ordinary differential equations, which can be treated using center manifold theory, the author explains very nicely the derivation and treatment of the resulting modulation equations. The methods are applied to the dynamics of interface solutions bifurcating in certain reaction-diffusion systems, which are modelled by the Allen-Cahn equation.