Abstract
The main object of study is the stochastic Cauchy problem for a quasilinear equation with random disturbances in the form of a Hilbert-valued white noise process and with an operator generating an integrated semigroup in the space L2(R). We use the Colombeau theory of multiplication of distributions to introduce an abstract stochastic factor algebra and construct an approximate solution of the problem in this algebra.
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Original Russian Text © I.V. Melnikova, V.A. Bovkun, U.A. Alekseeva, 2017, published in Differentsial’nye Uravneniya, 2017, Vol. 53, No. 12, pp. 1653–1663.
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Melnikova, I.V., Bovkun, V.A. & Alekseeva, U.A. Solution of Quasilinear Stochastic Problems in Abstract Colombeau Algebras. Diff Equat 53, 1605–1615 (2017). https://doi.org/10.1134/S0012266117120084
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DOI: https://doi.org/10.1134/S0012266117120084