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Singular evolution problems, regularization, and applications to physics, engineering, and biology. (English) Zbl 0884.34002

Janas, Jan (ed.) et al., Linear operators. Proceedings of the semester organized at the Stefan Banach International Mathematical Center, Warsaw, Poland, February 7–May 15, 1994. Warsaw: Polish Academy of Sciences, Inst. of Mathematics, Banach Cent. Publ. 38, 205-216 (1997).
This is a survey article on the evolution problems of the type \[ u'= Au+F(t),\quad u(0)= f, \] where \(A\) is a closed linear operator acting on the Banach space \(X\) and \(F\in L^1_{\text{loc}}([0, a],X)\). More precisely it deals with singular problems, in particular with problems not regular at \(t=0\). The author describes briefly some of the methods and results recently developed. This article in more detailed and completed form will be published elsewhere.
For the entire collection see [Zbl 0863.00036].

MSC:

34-02 Research exposition (monographs, survey articles) pertaining to ordinary differential equations
34G10 Linear differential equations in abstract spaces
47D06 One-parameter semigroups and linear evolution equations
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