江苏省应用数学（中国矿业大学）中心系列学术报告
报告题目：Statistical solutions and Liouville theorem for the second order lattice systems with varying coefficients
报告人：赵才地教授
报告时间：2023/11/29 （周三）09:00-10:00
腾讯会议：5318371238
报告摘要：In this talk, we first introduce the backgrounds and motivations concerning the invariant measures and statistical solutions. Then we verify the global well-posedness of the second order lattice systems with varying coefficients, and prove that the solution mappings form a continuous process on the time-dependent phase spaces and that the process has a time-dependent pullback attractor. Afterwards, we establish that there exists a family of Borel probability measures carried by the time-dependent pullback attractor which possesses invariant property under the action of the process. Further, we formulate the definition of statistical solution for the addressed evolution equations on time-dependent phase spaces and prove its existence. Finally, we reveal that the statistical solution of the second order lattice systems with varying coefficients satisfies the Liouville theorem in Statistical Mechanics.
报告人简介：赵才地，温州大学特聘教授，浙江省新世纪人才，温州市科技创新领军人才，主要从事非线性发展方程——无穷维动力系统方面得研究，从无穷维动力系统的途径研究非线性发展方程的不变测度和统计解，在一些典型非线性偏微分方程的统计解、轨道统计解以及随机微分方程的不变样本测度等方面取得若干成果，在《J. Differential Equations》、《Nonlinearity》、《Adv. Differential Equations》、《Science China： Math》等期刊上发表论文50余篇，主持国家自然科学基金面上项目3项，青年基金和天元基金各一项，浙江省自然科学基金面上项目2项，中国博士后科学基金1项，曾获浙江省自然科学三等奖，浙江省首届自然科学学术二等奖。