应数学与统计学院邀请，贵州师范大学王仁海教授将于2025年6月14-16日访问学院和甘肃省数学与统计学基础学科研究中心，并于6月15日作专题学术报告。
报告题目：On a Class of Fractional (α,p)-Laplacian Equations Driven by Superlinear Noise on R^d
报告摘要：We consider a wide class of fractional (α,p)-Laplacian equations on R^d driven by infinite-dimensional superlinear noise. The model has three striking features: a general fractional (α,p)-Laplace operator defined via a symmetric and translation invariant kernel function K^α_p with α ∈ (0,1) and p > 2; a polynomial drift growing at an arbitrary rate q −1 with q > 2; and a locally Lipschitz diffusion term with superlinear growth. By using a locally monotone method and a domain approximation argument, we first establish the global-in-time well-posedness and the higher-order Itô’s energy equations when the diffusion term has a superlinear growth rate less than p/2 or q/2. We then prove the existence and derive the moment estimates of invariant measures of the equation under further assumptions on the superlinear diffusion terms. When the damping coefficient is suitably large, we show the uniqueness, ergodicity as well as the Wasserstein exponential mixing of invariant measures without adding any additional conditions on the superlinear noise.The idea of uniform tail-estimates is used to overcome the difficulties caused by the lack of compactness of Sobolev embeddings on unbounded domains. The dissipativeness of the drift terms and some appropriate stopping times are used to carefully deal with the superlinear diffusion terms. The analysis has no any restrictions on α ∈ (0,1), d ∈ N, p > 2 or q > 2.This is a joint work with Professors Bixiang Wang and Penyu Chen.
报告时间：2025年6月15日16:30
报告地点：致勤楼D07会议室
邀请人：张旭萍 云亭教授
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报告人简介
王仁海，贵州师范大学特聘教授、博士生导师，西南大学与美国New Mexico Institute of Mining and Technology联合培养博士，北京应用物理与计算数学研究博士后，长期从事确定和随机无穷维动力系统理论及应用的研究。主持国家自然科学基金青年项目和数学天元项目以及中国博士后科学基金特别资助和面上资助，获重庆市优秀博士学位论文称号，入选贵州省科学技术协会首届青年人才托举工程，其论文发表于《Math. Ann.》、《Math. Mod. Meth. Appl. Sci.》、《Int. Math Res. Notice》与《SIAM J. Math. Anal.》等刊物。
数学与统计学院
甘肃省数学与统计学基础学科研究中心
2025年6月11日
