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Existence of strong solutions to singular nonlinear evolution equations. (English) Zbl 0592.34042
The author is concerned with the following problem: Suppose that the abstract Cauchy problem $$du/dt+A(t)u(t)\ni 0$$, $$s<t<T$$, $$u(s)=x$$ has a strong solution for $$0<s$$. Will there also exist a solution for $$s=0 ?$$ Sufficient conditions are given for an affirmative answer that still allows A(t) to be singular at $$t=0$$. The conditions require A(t) to be m- accretive for each fixed t and regular in t (in a certain sense) as t varies. Examples are given to show that no solution exists for $$s=0$$ if the conditions are not met. The conditions are illustrated by some examples of partial differential equations.
Reviewer: G.F.Webb

##### MSC:
 34G20 Nonlinear differential equations in abstract spaces
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