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

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  • Marat V. Markin

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.

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  • Marat V. Markin, 2011. "On the Differentiability of Weak Solutions of an Abstract Evolution Equation with a Scalar Type Spectral Operator," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2011, pages 1-27, May.
    • Handle: RePEc:hin:jijmms:825951
    DOI: 10.1155/2011/825951
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    1. Marat V. Markin, 2018. "On the Differentiability of Weak Solutions of an Abstract Evolution Equation with a Scalar Type Spectral Operator on the Real Axis," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2018, pages 1-14, July.

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