Generalized evolution operators and (generalized) \(C\)-semigroups. (English) Zbl 0748.47037

Lumer, Günter

Semigroup theory and evolution equations, Proc. 2nd Int. Conf., Delft/Neth. 1989, Lect. Notes Pure Appl. Math. 135, 337-345 (1991).

[For the entire collection see Zbl 0741.00048.]
The author investigates generalized solutions of the evolution equation \[ du/dt=Au+F(t),\quad u(0)=f,\quad F\in L^ 1_{\text{loc}}([0,\infty),B) \] in a Banach space \(B\) and corresponding (generally unbounded) evolution operators.

Reviewer: M.Perelmuter (Kiev)

MSC:

47D06

One-parameter semigroups and linear evolution equations

Keywords:

unbounded evolution operators; generalized solutions of the evolution equation