In this paper,we study Liouville theorem for the 3D stationary Q-tensor system of liquid crystal in Lorentz and Morrey spaces.Under some additional hypotheses,stated in terms of Lorentz and Morrey spaces,using energy ...In this paper,we study Liouville theorem for the 3D stationary Q-tensor system of liquid crystal in Lorentz and Morrey spaces.Under some additional hypotheses,stated in terms of Lorentz and Morrey spaces,using energy estimation,we obtain that the trivial solution u=Q=0 is the unique solution.Our theorems correspond to improvements of some recent results and contain some known results as particular cases.展开更多
This paper focuses on the investigation of a hyperbolic Kirchhoff equation with nonlinear damping and higher-order dissipation terms.Initially,the existence and uniqueness of local weak solutions are rigorously establ...This paper focuses on the investigation of a hyperbolic Kirchhoff equation with nonlinear damping and higher-order dissipation terms.Initially,the existence and uniqueness of local weak solutions are rigorously established.Next,within the framework of potential well theory,the classification of solution behaviors,including blow-up and global existence,is systematically analyzed according to the relationships among the exponents of nonlinear source terms.Finally,explicit bounds for the blow-up time and decay estimates for global solutions are presented.展开更多
基金Foundation item: Supported by important study project of the National Natural Science Foundation of China (No. 90211004) by the "Hundred Talent Project" of Chinese Academy of Sciences.
基金Supported by National Natural Science Foundation of China(11871305,11901346).
文摘In this paper,we study Liouville theorem for the 3D stationary Q-tensor system of liquid crystal in Lorentz and Morrey spaces.Under some additional hypotheses,stated in terms of Lorentz and Morrey spaces,using energy estimation,we obtain that the trivial solution u=Q=0 is the unique solution.Our theorems correspond to improvements of some recent results and contain some known results as particular cases.
基金Supported by Shandong Provincial Natural Science Foundation of China(Grant No.ZR2021MA003)。
文摘This paper focuses on the investigation of a hyperbolic Kirchhoff equation with nonlinear damping and higher-order dissipation terms.Initially,the existence and uniqueness of local weak solutions are rigorously established.Next,within the framework of potential well theory,the classification of solution behaviors,including blow-up and global existence,is systematically analyzed according to the relationships among the exponents of nonlinear source terms.Finally,explicit bounds for the blow-up time and decay estimates for global solutions are presented.
