On the Differentiability of Weak Solutions of an Abstract Evolution Equation with a Scalar Type Spectral Operator | Zendy

Marat V. Markin | Zendy

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

Author(s) -

Marat V. Markin

Publication year - 2011

Publication title -

international journal of mathematics and mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.21

H-Index - 39

eISSN - 1687-0425

pISSN - 0161-1712

DOI - 10.1155/2011/825951

Subject(s) - mathematics , differentiable function , banach space , smoothness , evolution equation , scalar (mathematics) , operator (biology) , mathematical analysis , type (biology) , pure mathematics , ecology , biochemistry , chemistry , geometry , repressor , biology , transcription factor , gene

For the evolution equation ()=() with a scalar type spectral operator in a Banach space, conditions on are found that are necessary and sufficient for all weak solutions of the equation on [0,∞) to be strongly infinite differentiable on [0,∞) or [0,∞). Certain effects of smoothness improvement of the weak solutions are analyzed.

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