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題目：Large Deviations of Fractional Stochastic Equations on Unbounded Domains

報告人：王碧祥,  New Mexico Institute of Mining and Technology,  教授

時間:  05月28日（周二）下午15: 30-16: 30

地點：30456

摘要：In this talk, we discuss the large deviation principle of the non-local fractional stochastic reaction-diffusion equations with a polynomial drift of arbitrary degree driven by multiplicative noise defined on unbounded domains. We first prove the strong convergence of the solutions of a control equation with respect to the weak topology of controls, and then show the convergence in distribution of the solutions of the stochastic equation when the noise intensity approaches zero. We finally establish the large deviations of the stochastic equation by the weak convergence method. The main difficulty of the paper is caused by the non-compactness of Sobolev embeddings on unbounded domains, and the idea of uniform tail-ends estimates is employed to circumvent the obstacle in order to obtain the tightness of distribution laws of the stochastic equation and the precompactness of the control equation.

個人簡介：王碧祥，美國新墨西哥礦業(yè)理工大學數學系終身教授，主要從事無窮維動力系統(tǒng)和非線性偏微分方程理論與應用等領域的研究。目前已發(fā)表SCI 論文150余篇，研究主要成果發(fā)表于《Mathematische Annalen》,《Transactions of the American Mathematical Society》,《Journal of Functional Analysis》,《SIAM Journal on Applied Dynamical Systems》，《Proceedings of the American Mathematical Society》,《Journal of Differential Equations》,《Science China Mathematics》,《Stochastic Processes and their Applications 》,《Nonlinearity》,《Physica D: Nonlinear Phenomena》,《Journal of Dynamics and Differential Equations》等多個國際知名數學學術期刊上。

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