In this note, we investigated existence and uniqueness of entropy solution for triply nonlinear degenerate parabolic problem with zero-flux boundary condition. Accordingly to the case of doubly nonlinear degenerate pa...In this note, we investigated existence and uniqueness of entropy solution for triply nonlinear degenerate parabolic problem with zero-flux boundary condition. Accordingly to the case of doubly nonlinear degenerate parabolic hyperbolic equation, we propose a generalization of entropy formulation and prove existence and uniqueness result without any structure condition.展开更多
We investigate the uniform regularity and zero kinematic viscosity-magnetic diffusion limit for the incompressible viscous magnetohydrodynamic equations with the Navier boundary conditions on the velocity and perfectl...We investigate the uniform regularity and zero kinematic viscosity-magnetic diffusion limit for the incompressible viscous magnetohydrodynamic equations with the Navier boundary conditions on the velocity and perfectly conducting conditions on the magnetic field in a smooth bounded domain Ω⊂R^(3).It is shown that there exists a unique strong solution to the incompressible viscous magnetohydrodynamic equations in a finite time interval which is independent of the viscosity coefficient and the magnetic diffusivity coefficient.The solution is uniformly bounded in a conormal Sobolev space and W^(1,∞)(Ω)which allows us to take the zero kinematic viscosity-magnetic diffusion limit.Moreover,we also get the rates of convergence in L^(∞)(0,T;L^(2)),L^(∞)(0,T;W^(1,p))(2≤p<∞),and L^(∞)((0,T)×Ω)for some T>0.展开更多
The present work studies the inverse scattering transforms(IST)of the inhomogeneous fifth-order nonlinear Schrodinger(NLS)equation with zero boundary conditions(ZBCs)and nonzero boundary conditions(NZBCs).Firstly,the ...The present work studies the inverse scattering transforms(IST)of the inhomogeneous fifth-order nonlinear Schrodinger(NLS)equation with zero boundary conditions(ZBCs)and nonzero boundary conditions(NZBCs).Firstly,the bound-state solitons of the inhomogeneous fifth-order NLS equation with ZBCs are derived by the residue theorem and the Laurent's series for the first time.Then,by combining with the robust IST,the Riemann-Hilbert(RH)problem of the inhomogeneous fifth-order NLS equation with NZBCs is revealed.Furthermore,based on the resulting RH problem,some new rogue wave solutions of the inhomogeneous fifth-order NLS equation are found by the Darboux transformation.Finally,some corresponding graphs are given by selecting appropriate parameters to further analyze the unreported dynamic characteristics of the corresponding solutions.展开更多
This paper studies the weighted Hardy inequalities on the discrete intervals with four different kinds of boundary conditions. The main result is the uniform expression of the basic estimate of the optimal constant wi...This paper studies the weighted Hardy inequalities on the discrete intervals with four different kinds of boundary conditions. The main result is the uniform expression of the basic estimate of the optimal constant with the corresponding boundary condition. Firstly, one-side boundary condition is considered, which means that the sequences vanish at the right endpoint （ND-case）. Based on the dual method, it can be translated into the case vanishing at left endpoint （DN-case）. Secondly, the condition is the case that the sequences vanish at two endpoints （DD-case）. The third type of condition is the generality of the mean zero condition （NN-case）, which is motivated from probability theory. To deal with the second and the third kinds of inequalities, the splitting technique is presented. Finally, as typical applications, some examples are included.展开更多
文摘In this note, we investigated existence and uniqueness of entropy solution for triply nonlinear degenerate parabolic problem with zero-flux boundary condition. Accordingly to the case of doubly nonlinear degenerate parabolic hyperbolic equation, we propose a generalization of entropy formulation and prove existence and uniqueness result without any structure condition.
基金supported partially by NSFC(11671193,11971234)supported partially by the China Postdoctoral Science Foundation(2019M650581).
文摘We investigate the uniform regularity and zero kinematic viscosity-magnetic diffusion limit for the incompressible viscous magnetohydrodynamic equations with the Navier boundary conditions on the velocity and perfectly conducting conditions on the magnetic field in a smooth bounded domain Ω⊂R^(3).It is shown that there exists a unique strong solution to the incompressible viscous magnetohydrodynamic equations in a finite time interval which is independent of the viscosity coefficient and the magnetic diffusivity coefficient.The solution is uniformly bounded in a conormal Sobolev space and W^(1,∞)(Ω)which allows us to take the zero kinematic viscosity-magnetic diffusion limit.Moreover,we also get the rates of convergence in L^(∞)(0,T;L^(2)),L^(∞)(0,T;W^(1,p))(2≤p<∞),and L^(∞)((0,T)×Ω)for some T>0.
基金supported by the National Natural Science Foundation of China under Grant No.11975306the Natural Science Foundation of Jiangsu Province under Grant No.BK20181351+1 种基金the Six Talent Peaks Project in Jiangsu Province under Grant No.JY-059the Fundamental Research Fund for the Central Universities under the Grant Nos.2019ZDPY07 and 2019QNA35。
文摘The present work studies the inverse scattering transforms(IST)of the inhomogeneous fifth-order nonlinear Schrodinger(NLS)equation with zero boundary conditions(ZBCs)and nonzero boundary conditions(NZBCs).Firstly,the bound-state solitons of the inhomogeneous fifth-order NLS equation with ZBCs are derived by the residue theorem and the Laurent's series for the first time.Then,by combining with the robust IST,the Riemann-Hilbert(RH)problem of the inhomogeneous fifth-order NLS equation with NZBCs is revealed.Furthermore,based on the resulting RH problem,some new rogue wave solutions of the inhomogeneous fifth-order NLS equation are found by the Darboux transformation.Finally,some corresponding graphs are given by selecting appropriate parameters to further analyze the unreported dynamic characteristics of the corresponding solutions.
基金Supported by NSFC(Grant No.11131003)the “985” project from the Ministry of Education in China
文摘This paper studies the weighted Hardy inequalities on the discrete intervals with four different kinds of boundary conditions. The main result is the uniform expression of the basic estimate of the optimal constant with the corresponding boundary condition. Firstly, one-side boundary condition is considered, which means that the sequences vanish at the right endpoint （ND-case）. Based on the dual method, it can be translated into the case vanishing at left endpoint （DN-case）. Secondly, the condition is the case that the sequences vanish at two endpoints （DD-case）. The third type of condition is the generality of the mean zero condition （NN-case）, which is motivated from probability theory. To deal with the second and the third kinds of inequalities, the splitting technique is presented. Finally, as typical applications, some examples are included.
基金Supported by the National Natural Science Foundation of China (11071053)the Natural Science Foundation of Hebei Province (A2010001482)the Key Project of Science and Research of Hebei Education Department (ZH2012080)
