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Time-dependent implicit evolution equations. (English) Zbl 0603.47038

Existence and uniqueness theorems are developed for Cauchy problems corresponding to abstract equations of the form \[ \frac{d}{dt}(B(t)U(t))+AU(t)=f(t) \] whre B(t) is a time dependent family of linear, possibly degenerate operators and A is a nonlinear, possibly time dependent operator. The results presented here improve earlier papers by relaxing the coercivity assumption on A and by eliminating technical assumptions on the square root of the closure of the operators B(t).

MSC:

47E05 General theory of ordinary differential operators
47F05 General theory of partial differential operators
34G10 Linear differential equations in abstract spaces
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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