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發布時間:2021-05-27【告訴好友】 【關閉窗口】





報告人: 楊志堅?教授 (鄭州大學)

報告題目:Regular solutions and strong attractors for the Kirchhoff wave model with structural ?nonlinear damping


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.



楊志堅 ?鄭州大學理學博士,日本九州大學數理學博士,鄭州大學2級教授,博士生導師,河南省跨世紀學術、技術帶頭人,河南省數學會常務理事,美國 《Mathematical Reviews》評論員,《Journal of Partial Differential Equations》期刊編委。主要研究非線性發展方程的整體適定性及對應的無窮維耗散動力系統的長時間動力學行為。主持完成多項國家自然科學基金面上項目;已在JDE,Nonlinearity,DCDS,中國科學,等國內外SCI期刊上發表論文70多篇。獲得河南省科技進步二等獎1項。