Mean flow properties for equatorially trapped internal water wave–current interactions

The aim of this paper is to provide an analysis of the mean flow velocities, and the related mass transport induced by equatorially trapped internal water waves with a constant underlying current.     

带有Sobolev-Hardy临界指标项的非齐次椭圆方程的解

考虑带有Hardy和Sobolev-Hardy临界指标项的非齐次椭圆方程{-Δu-u(u/(|x|~2))=λu+(((|u|~(2~*(s)-2))/(|x|~s))u+f,在Ω中,u=0,在Ω上,这里2~*(s)=(2(N-s))/(N-2)是临界Sobolev-Hardy指标,N≥3,0≤s2,0≤μ=((N-2)~2)/4,ΩR~N是一个开区域.假设0≤λ≤λ_1时,λ_1是正算子-△-μ/(|x|~2)的第一特征值.f∈H~1_0(Ω)~*,f(x)≠0.当f满足适当的条件时,此方程在H~1_0(Ω)中至少具有两个解u_0和u_1.而且,当f≥0时,有u_0≥0和u_1≥0.     

Exact and approximation product solutions form of heat equation with nonlocal boundary conditions using Ritz–Galerkin method with Bernoulli polynomials basis

In this article, a new method is introduced for finding the exact solution of the product form of parabolic equation with nonlocal boundary conditions. Approximation solution of the present problem is implemented by the Ritz–Galerkin method in Bernoulli polynomials basis. The properties of Bernoulli polynomials are first presented, then Ritz–Galerkin method in Bernoulli polynomials is used to reduce the given differential equation to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the techniques presented in this article for finding the exact and approximation solutions. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1143–1158, 2017     

Exact controllability of nodal profile for 1‐D first order quasilinear hyperbolic systems with internal controls

For 1‐D first order quasilinear hyperbolic systems without zero eigenvalues, based on the theory of exact boundary controllability of nodal profile, using an extension method, the exact controllability of nodal profile can be realized in a shorter time by means of additional internal controls acting on suitably small space‐time domains. On the other hand, using a perturbation method, the exact controllability of nodal profile for 1‐D first order quasilinear hyperbolic systems with zero eigenvalues can be realized by additional internal controls to the part of equations corresponding to zero eigenvalues. Furthermore, by adding suitable internal controls to all the equations on suitable domains, the exact controllability of nodal profile for systems with zero eigenvalues can be realized in a shorter time.     

Analysis of an elasto-piezoelectric system of hemivariational inequalities with thermal effects

In this paper we prove the existence and uniqueness of a weak solution for a dynamic electo-viscoelastic problem that describes a contact between a body and a foundation. We assume the body is made from thermoviscoelastic material and consider nonmonotone boundary conditions for the contact. We use recent results from the theory of hemivariational inequalities and the fixed point theory.     

Local regularity criteria of a suitable weak solution to MHD equations

We present a regularity condition of a suitable weak solution to the MHD equations in three dimensional space with slip boundary conditions for a velocity and magnetic vector fields. More precisely, we prove a suitable weak solution are H¨older continuous near boundary provided that the scaled mixed L_(x,t)~(p,q) -norm of the velocity vector field with 3/p + 2/q ≤ 2,2 q ∞ is sufficiently small near the boundary. Also, we will investigate that for this solution u ∈ L_(x,t)~(p,q) with 1≤3/p+2/q≤3/2, 3 p ∞, the Hausdorff dimension of its singular set is no greater than max{p, q}(3/p+2/q-1).     

On entire solutions of two types of systems of complex differential-difference equations

In this paper, we will mainly investigate entire solutions with finite order of two types of systems of differential-difference equations, and obtain some interesting results. It extends some results concerning complex differential (difference) equations to the systems of differential-difference equations.     

Renormalized solutions of elliptic equations with Robin boundary conditions

In the present paper, we consider elliptic equations with nonlinear and nonhomogeneous Robin boundary conditions of the type{-div(B(x, u)▽u) = f in ?,u = 0 on Γ_0,B(x, u)▽u·n→+γ(x)h(u) =g on Γ_1,where f and g are the element of L~1(?) and L~1(Γ_1), respectively. We define a notion of renormalized solution and we prove the existence of a solution. Under additional assumptions on the matrix field B we show that the renormalized solution is unique.     

一类双曲型方程的Hamilton算子半群方法

将一类双曲型方程混合问题转换成一阶抽象Cauchy问题,证明所得Hamilton算子矩阵H在相应空间中生成压缩半群,并借助Fourier变换,采用一致连续半群做逼近的方法,得到H所生成的压缩半群,进而给出了问题的古典解.