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On the wellposedness of nonautonomous second order Cauchy problems. (English) Zbl 0949.34045
The author studies the wellposedness of abstract second-order Cauchy problems of the form $$u^{''}(t) = A(t)u^{'}(t) + B(t)u(t) + f(t)$$, $$0 \geq s \geq T$$, where $$A(t)$$ and $$B(t)$$ are linear operators on a Banach space. By reducing the problem to a first-order system he obtains sufficient conditions which can be applied to nonautonomous partial differential equations.

##### MSC:
 34G10 Linear differential equations in abstract spaces 35G10 Initial value problems for linear higher-order PDEs