讲座题目：Regular solutions and strong attractors for the Kirchhoff wave model with structural  nonlinear damping

主办单位：长江大学信息与数学学院

报告专家：杨志坚（郑州大学 教授）

报告时间：2021年12月6（周一） 9:00-11:00

腾讯会议ID：930 225 651

专家简介：杨志坚  郑州大学理学博士，日本九州大学数理学博士，郑州大学2级教授，博士生导师，河南省跨世纪学术、技术带头人, 美国 《Mathematical Reviews》评论员，《Journal of Partial Differential Equations》期刊编委。主要研究非线性发展方程的整体适定性及对应的无穷维耗散动力系统的长时间动力学行为。主持完成4项国家自然科学基金面上项目；已在《J. Differential Equations》、《Nonlinearity》、《Commun. Contemp. Math.》、《J. Dyn. Differ. Equ.》、《Discrete Contin. Dyn. Syst.》等国内外SCI期刊上发表研究论文90篇。获得河南省科技进步二等奖1项。

Abstract: In this talk, we investigate the well-posedness and longtime dynamics of the  Kirchhoff wave model with structural nonlinear damping. We find a new critical exponent and show that  when the growth exponent of the nonlinearity is of the optimal growth: (i) the IBVP of the equation is well-posed and its weak solution is just the strong one; (ii) the related solution semigroup has a strong global attractor and an strong exponential attractor, whose compactness, boundedness of the fractal dimension and the attractiveness are all in the topology of the strong solution space, respectively;  (iii) the family of global attractors is upper semi-continuous on the perturbation parameter in the topology of the strong solution space. These results break though the longstanding existed growth restriction for the uniqueness index, deepen and extend the results in recent literatures.