江蘇省應用數學（中國礦業大學）中心系列學術報告
報告題目：Statistical solutions and Liouville theorem for the second order lattice systems with varying coefficients
報告人：趙才地教授
報告時間：2023/11/29 （周三）09:00-10:00
騰訊會議：5318371238
報告摘要：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.
報告人簡介：趙才地，溫州大學特聘教授，浙江省新世紀人才，溫州市科技創新領軍人才，主要從事非線性發展方程——無窮維動力系統方面得研究，從無窮維動力系統的途徑研究非線性發展方程的不變測度和統計解，在一些典型非線性偏微分方程的統計解、軌道統計解以及随機微分方程的不變樣本測度等方面取得若幹成果，在《J. Differential Equations》、《Nonlinearity》、《Adv. Differential Equations》、《Science China： Math》等期刊上發表論文50餘篇，主持國家自然科學基金面上項目3項，青年基金和天元基金各一項，浙江省自然科學基金面上項目2項，中國博士後科學基金1項，曾獲浙江省自然科學三等獎，浙江省首屆自然科學學術二等獎。