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This article is cited in 21 scientific papers (total in 21 papers)
Mathematical Modelling
Exponential dichotomies in Barenblatt– Zheltov–Kochina model in spaces of differential forms with “noise”
O. G. Kitaeva, D. E. Shafranov, G. A. Sviridyuk South Ural State University, Chelyabinsk, Russian Federation
Abstract:
We investigate stability of solutions in
linear stochastic Sobolev type models with the relatively bounded operator in spaces of smooth differential forms
defined on smooth compact oriented Riemannian manifolds without boundary. To this end, in the space of differential forms,
we use the pseudo-differential Laplace–Beltrami operator instead of the usual Laplace operator.
The Cauchy condition and the Showalter–Sidorov condition are used as the initial conditions. Since “white noise”
of the model is non-differentiable in the usual sense, we use the derivative of stochastic process in the sense of Nelson–Gliklikh.
In order to investigate stability of solutions, we establish existence of exponential dichotomies dividing the space of solutions into stable
and unstable invariant subspaces. As an example, we use a stochastic version of the Barenblatt–Zheltov–Kochina equation in the space of differential
forms defined on a smooth compact oriented Riemannian manifold without boundary.
Keywords:
Sobolev type equations, differential forms, stochastic equations, Nelson–Gliklikh derivative.
Received: 24.12.2018
Citation:
O. G. Kitaeva, D. E. Shafranov, G. A. Sviridyuk, “Exponential dichotomies in Barenblatt– Zheltov–Kochina model in spaces of differential forms with “noise””, Vestnik YuUrGU. Ser. Mat. Model. Progr., 12:2 (2019), 47–57
Linking options:
https://www.mathnet.ru/eng/vyuru487 https://www.mathnet.ru/eng/vyuru/v12/i2/p47
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Abstract page: | 207 | Full-text PDF : | 66 | References: | 34 |
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