On the Differentiability of Weak Solutions of an Abstract Evolution Equation with a Scalar Type Spectral Operator on the Real Axis

Autor: Marat V. Markin
Jazyk: angličtina
Rok vydání: 2018
Předmět:
Zdroj: International Journal of Mathematics and Mathematical Sciences, Vol 2018 (2018)
Druh dokumentu: article
ISSN: 0161-1712
1687-0425
DOI: 10.1155/2018/4168609
Popis: Given the abstract evolution equation y′(t)=Ay(t), t∈R, with scalar type spectral operator A in a complex Banach space, found are conditions necessary and sufficient for all weak solutions of the equation, which a priori need not be strongly differentiable, to be strongly infinite differentiable on R. The important case of the equation with a normal operator A in a complex Hilbert space is obtained immediately as a particular case. Also, proved is the following inherent smoothness improvement effect explaining why the case of the strong finite differentiability of the weak solutions is superfluous: if every weak solution of the equation is strongly differentiable at 0, then all of them are strongly infinite differentiable on R.
Databáze: Directory of Open Access Journals
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