应兰州交通大学数理学院张建刚院长和周文学教授邀请,贵州师范大学王仁海教授将于2025年6月14-16日与我系相关师生进行学术研讨,并于6月15日上午举行学术报告,欢迎各位老师和研究生同学参加。

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.

时间：6月15日8:30-10:00

地点：8-D-311

专家简介：

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。

“天佑数学讲坛”由兰州交通大学数理学院发起创办,是数理学院数学系高层次常态化的学术交流平台。 讲坛将不定期邀请国内外知名学者围绕数学国际前沿动态展开学术交流与探讨,通过学术报告、小型研讨会等形式为数学系师生提供向国内外知名学者学习的机会,以便能够及时准确地了解数学领域的前沿学术信息,进一步提升数学系师生的学术视野及科研水平。

数理学院

甘肃省复杂系统分析及控制基础学科研究中心

2025年5月11日