Non-local Stochastic Evolutionary Systems: Theory and Applications
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Organizer(s): |
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Affiliation:
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Country:
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Hao Tang
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Tianjin University
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Peoples Rep of China
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Kenneth Karlsen
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University of Oslo
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Norway
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Feng-Yu Wang
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Tianjin University
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Peoples Rep of China
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Introduction:
| | This special session will explore non-local phenomena in stochastic evolutionary systems, with a particular emphasis on two important research directions: stochastic (partial) differential equations with non-locality in sample variables, and stochastic partial differential equations with non-locality in spatial variables. Discussions will span theoretical analysis, computational methods, and practical applications.
The first direction focuses on systems such as McKean–Vlasov equations, which exhibit strong dependence on the probability distribution of solutions and provide a probabilistic framework for studying nonlinear Fokker–Planck equations and nonlinear Markov processes. Key topics include functional inequalities, asymptotic behavior of empirical measures under the Wasserstein-type metric, and systems driven by Lévy processes.
The second direction concerns equations arising in applied contexts such as fluid dynamics, where non-local components—such as the pressure term—play an essential role. Discussions will emphasize non-local dissipative structures, transport mechanisms, and non-local random noise. Special attention will be devoted to mean-field stochastic fluid models that incorporate both distributional dependence and spatial non-locality. These hybrid models, which integrate dual non-local mechanisms, represent a rapidly advancing frontier in interdisciplinary research.
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