Abstract Evolution Equations, Periodic Problems and Applications

The book is an introduction to abstract semi-linear evolution equations of parabolic type, with special emphasis on periodic problems. Throughout, it makes use of the theory of interpolation spaces rather than fractional power spaces. While the use of fractional power spaces involves a lot of technicalities, the use of interpolation spaces allows a much more elegant and complete treatment of semi-linear problems, particularly for non-autonomous equations. At the same time it brings more conceptual clarity. It is then shown how these abstract results can be applied to concrete reaction-diffusion equations and systems