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

Marat V. Markin

International Journal of Mathematics and Mathematical Sciences, 2011, vol. 2011, 1-27

Abstract:

For the evolution equation 𠑦 î…ž ( ð ‘¡ ) = ð ´ ð ‘¦ ( ð ‘¡ ) with a scalar type spectral operator ð ´ in a Banach space, conditions on ð ´ 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.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:825951

DOI: 10.1155/2011/825951

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