When we talk about evolution equation the first idea who comes to the mind is the semigroups theory, this theory deals with the Cuachy problems of the form $$\frac{{\partial u}}{{\partial t}} = Au$$ where $A$ is an operator acts ob Banach spaces to another. My question is  : is there any theory which deals with the evolution problems of the form $$\frac{{\partial u}}{{\partial t}} = A(t)u$$ this time $A$ depends on $t$  ? thank you.

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 $t$?