I recently learned how to prove the following theorem due to Floquet:
Let $\Phi(t)$ be a fundamental matrix solution $\Phi(t)$ of the equation $\Phi' = A(t) \Phi(t)$ ($*$), where $A(t)$ is periodic with minimal period $p$. Then $\Phi(t+p)$ is also a fundamental solution of ($*$) and there exists an invertible matrix $P(t)$ with periodicity $p$ and a matrix $B$ such that $\Phi(t) = P(t) \exp(Bt)$.
Obviously, this is useful to be able to understand properties of the solutions of the ODE system.
On the other hand, I have seen Floquet theory being used (for example here ) to study linear PDEs (in the paper the authors study a linearised form of Navier Stokes). Could someone point me to some reference where I could read up on the basics of Floquet theory for PDEs? I did find a book on the topic, but if possible, I would just like to study the basics and am afraid the book may be overly technical. If someone has read the book and can comment on it, I would be very happy as well.
