When we talk about evolution equation the first idea that comes to the mind is the semigroups theory. This theory deals with Cauchy problems of the form $$\frac{{\partial u}}{{\partial t}} = Au,$$ where $A$ is an operator on Banach spaces. My question is: is there any theory which deals with evolution problems of the form $$\frac{{\partial u}}{{\partial t}} = A(t)u,$$ where now $A$ may depend on $t$?
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2$\begingroup$ You could fill libraries with that, for example start here: books.google.com/books/about/… $\endgroup$– Christian RemlingCommented Nov 1, 2017 at 23:13
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1$\begingroup$ Multiplicative ergodic theory is highly relevant, providing the time dependence of $A(t)$ is stationary. $\endgroup$– Anthony QuasCommented Nov 2, 2017 at 2:11
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1 Answer
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You can see these two books:
1) Daniel Daners and Pablo Koch Medina: Abstract evolution equations, periodic problems and applications
2) Peter Hess: Periodic-Parabolic Boundary Value Problems and Positivity
