This paper deals with quasilinear elliptic equations of singular growth like-Δu-uΔ(u^(2))=a(x)u^(-1).We establish the existence of positive solutions for general a(x)∈L^(p)(Ω),p>2,whereΩis a bounded domain inℝ...This paper deals with quasilinear elliptic equations of singular growth like-Δu-uΔ(u^(2))=a(x)u^(-1).We establish the existence of positive solutions for general a(x)∈L^(p)(Ω),p>2,whereΩis a bounded domain inℝ^(N)with N≥1.展开更多
Let n be any positive integer, and S（n） be the cubic complements of n. The main purpose of this paper is to study the asymptotic of ∑n≤x（n/S（n））^k （k ≥ 1）. And by using the elementary methods, it intends to...Let n be any positive integer, and S（n） be the cubic complements of n. The main purpose of this paper is to study the asymptotic of ∑n≤x（n/S（n））^k （k ≥ 1）. And by using the elementary methods, it intends to give two sharper asymptotic formulas, and thus extends the related conclusions.展开更多
The conservation laws for the （1＋2）-dimensional Zakharov-Kuznetsov modified equal width （ZK-MEW） equation with power law nonlinearity are constructed by using Noether＇s approach through an interesting method of ...The conservation laws for the （1＋2）-dimensional Zakharov-Kuznetsov modified equal width （ZK-MEW） equation with power law nonlinearity are constructed by using Noether＇s approach through an interesting method of increasing the order of this equation. With the aid of an obtained conservation law, the generalized double reduction theorem is applied to this equation. It can be shown that the reduced equation is a second order nonlinear ODE. FinaJ1y, some exact solutions for a particular case of this equation are obtained after solving the reduced equation.展开更多
The power-law fluid flow past a row of uniform placed square cylinders is investigated using the Lattice Boltzmann method (LBM).The flow is assumed to be two-dimensional and incompressible.The relaxation time is assum...The power-law fluid flow past a row of uniform placed square cylinders is investigated using the Lattice Boltzmann method (LBM).The flow is assumed to be two-dimensional and incompressible.The relaxation time is assumed to be shear-dependent and determined by using a variable parameter related to the local shear rate.The effects of both shear-thinning/shear-thickening property and the cylinder spacing on the confluence of the jets are mainly concerned.The bifurcation diagrams of the flow are obtained,which include confluences of double and quadruple jets.The results show that both the first and second pitchfork bifurcations are advanced due to the effect of the shear-thinning property,and postponed due to the shear-thickening property.展开更多
In this paper, the time fractional Fordy–Gibbons equation is investigated with Riemann–Liouville derivative. The equation can be reduced to the Caudrey–Dodd–Gibbon equation, Savada–Kotera equation and the Kaup–K...In this paper, the time fractional Fordy–Gibbons equation is investigated with Riemann–Liouville derivative. The equation can be reduced to the Caudrey–Dodd–Gibbon equation, Savada–Kotera equation and the Kaup–Kupershmidt equation, etc. By means of the Lie group analysis method, the invariance properties and symmetry reductions of the equation are derived. Furthermore, by means of the power series theory, its exact power series solutions of the equation are also constructed. Finally, two kinds of conservation laws of the equation are well obtained with aid of the self-adjoint method.展开更多
基金Supported by National Science Foundation of China(11971027,12171497)。
文摘This paper deals with quasilinear elliptic equations of singular growth like-Δu-uΔ(u^(2))=a(x)u^(-1).We establish the existence of positive solutions for general a(x)∈L^(p)(Ω),p>2,whereΩis a bounded domain inℝ^(N)with N≥1.
文摘Let n be any positive integer, and S（n） be the cubic complements of n. The main purpose of this paper is to study the asymptotic of ∑n≤x（n/S（n））^k （k ≥ 1）. And by using the elementary methods, it intends to give two sharper asymptotic formulas, and thus extends the related conclusions.
基金Supported by the Fundamental Research Funds for the Central Universities under Grant No.2013XK03the National Natural Science Foundation of China under Grant No.11371361
文摘The conservation laws for the （1＋2）-dimensional Zakharov-Kuznetsov modified equal width （ZK-MEW） equation with power law nonlinearity are constructed by using Noether＇s approach through an interesting method of increasing the order of this equation. With the aid of an obtained conservation law, the generalized double reduction theorem is applied to this equation. It can be shown that the reduced equation is a second order nonlinear ODE. FinaJ1y, some exact solutions for a particular case of this equation are obtained after solving the reduced equation.
基金assistance from the Natural Science Foundation of China(GrantNo. 10972115)
文摘The power-law fluid flow past a row of uniform placed square cylinders is investigated using the Lattice Boltzmann method (LBM).The flow is assumed to be two-dimensional and incompressible.The relaxation time is assumed to be shear-dependent and determined by using a variable parameter related to the local shear rate.The effects of both shear-thinning/shear-thickening property and the cylinder spacing on the confluence of the jets are mainly concerned.The bifurcation diagrams of the flow are obtained,which include confluences of double and quadruple jets.The results show that both the first and second pitchfork bifurcations are advanced due to the effect of the shear-thinning property,and postponed due to the shear-thickening property.
基金Supported by the Fundamental Research Funds for Key Discipline Construction under Grant No.XZD201602the Fundamental Research Funds for the Central Universities under Grant Nos.2015QNA53 and 2015XKQY14+2 种基金the Fundamental Research Funds for Postdoctoral at the Key Laboratory of Gas and Fire Control for Coal Minesthe General Financial Grant from the China Postdoctoral Science Foundation under Grant No.2015M570498Natural Sciences Foundation of China under Grant No.11301527
文摘In this paper, the time fractional Fordy–Gibbons equation is investigated with Riemann–Liouville derivative. The equation can be reduced to the Caudrey–Dodd–Gibbon equation, Savada–Kotera equation and the Kaup–Kupershmidt equation, etc. By means of the Lie group analysis method, the invariance properties and symmetry reductions of the equation are derived. Furthermore, by means of the power series theory, its exact power series solutions of the equation are also constructed. Finally, two kinds of conservation laws of the equation are well obtained with aid of the self-adjoint method.
