Email this article Solution of Quasilinear Stochastic Problems in Abstract Colombeau Algebras
- Authors: Melnikova I.V.1, Bovkun V.A.1, Alekseeva U.A.1
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Affiliations:
- Ural Federal University
- Issue: Vol 53, No 12 (2017)
- Pages: 1605-1615
- Section: Partial Differential Equations
- URL: https://journal-vniispk.ru/0012-2661/article/view/154647
- DOI: https://doi.org/10.1134/S0012266117120084
- ID: 154647
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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.
About the authors
I. V. Melnikova
Ural Federal University
Author for correspondence.
Email: Irina.Melnikova@urfu.ru
Russian Federation, Yekaterinburg, 620002
V. A. Bovkun
Ural Federal University
Email: Irina.Melnikova@urfu.ru
Russian Federation, Yekaterinburg, 620002
U. A. Alekseeva
Ural Federal University
Email: Irina.Melnikova@urfu.ru
Russian Federation, Yekaterinburg, 620002
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