Abstract
In various distribution spaces, we study the Cauchy problem for the equation u′(t) = Au(t)+B \(\mathbb{W}\)(t), t ≥ 0, with a singular white noise \(\mathbb{W}\) and an operator A generating various regularized semigroups in a Hilbert space. Depending on the properties of the operator A, we construct solutions generalized separately and jointly with respect to the time, random, and “space” variables.
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Original Russian Text © I.V. Melnikova, 2013, published in Differentsial’nye Uravneniya, 2013, Vol. 49, No. 4, pp. 494–505.
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Melnikova, I.V. Generalized solutions of differential-operator equations with singular white noise. Diff Equat 49, 475–486 (2013). https://doi.org/10.1134/S0012266113040083
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DOI: https://doi.org/10.1134/S0012266113040083