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This article is cited in 8 scientific papers (total in 9 papers)
Stochastic interpretation of quasilinear parabolic systems with cross-diffusion
Ya. I. Belopol'skaya St. Petersburg State University of Architecture and Civil Engineering
Abstract:
We construct a stochastic interpretation of the generalized solution of the Cauchy problem for a strongly coupled system of quasilinear parabolic equations. To this end we derive a system of stochastic equations and prove that its solution allows us to construct a probabilistic representation of the original Cauchy problem solution and investigate its properties. Our construction of a probabilistic representation of the generalized solution of the Cauchy problem is crucially based on results of stochastic flow theory.
Received: 23.04.2015
Citation:
Ya. I. Belopol'skaya, “Stochastic interpretation of quasilinear parabolic systems with cross-diffusion”, Teor. Veroyatnost. i Primenen., 61:2 (2016), 268–299; Theory Probab. Appl., 61:2 (2017), 208–234
Linking options:
https://www.mathnet.ru/eng/tvp5056https://doi.org/10.4213/tvp5056 https://www.mathnet.ru/eng/tvp/v61/i2/p268
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Abstract page: | 464 | Full-text PDF : | 141 | References: | 66 | First page: | 19 |
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