粘弹性模型方程的整体光滑解

本文研究一个带张弛的弹性模型方程的整体光滑解．我们的结果表明，张弛具有耗散效应，它能保持“小”始值解的光滑性．     

粘弹性材料中一类非线性方程组的整体经典解

考虑具衰减记忆项的枯弹性材料中一类非线性方程组的Cauchy问题,在"大"初值条件下证明了经典解的整体存在性,给出了解在有限时间内产生奇性的充分条件,结果表明记忆具有耗散效应.     

一类具有双重奇性的抛物型方程的整体解和有限熄灭

本文讨论具有双重奇性的抛物型方程ｕｔ＝ ｄｉｖ（｜△ｕ~ａ｜ｐ~－２△ｕ~ａ）,（ｘ,ｔ） ∈ Ｒ~ｎ ×（０,∞）,其中Ｐ＞ １,ａ＞ ０,ｎ≤ ２．证明当１＜ Ｐ＜ｎ（ａ＋１）／（ａｎ＋１）时,存在整体自相似解ｕｇｓ（·,ｔ） ∈ Ｌ~ｑ（Ｒ~ｎ）（ｑ＞ｓ＝~△ｎ［１－ａ（ｐ－１）］／ｐ）,但是ｕｇｓ∈~／Ｌ~ｓ（Ｒ~ｎ）（定理２．１）;同时存在有限熄灭的自相似解ｕｌｓ满足相同的积分条件（定理 ３．１）．     

一类具有双重奇性的抛物型方程的整体解和有限熄灭

本文讨论具有双重奇性的抛物型方程ut=div(|uα|p-2uα),(x,t)∈R     

带粘弹性边界条件的耦合非线性波动方程组的整体可解性

本文讨论了两根非线性弹性杆的耦合问题，利用沿特征线积分与能量估计相结合的方法证明了在该系统一端及两杆之间用某一粘弹性单元连接时，具小初值的初边值问题存在整体经典解     

Euler-Bernoulli粘弹性方程初边值问题整体解的存在性

本文利用 Faedo- Galerkin方法证明了一类具记忆项的 Euler- Bernoulli粘弹性方程初边值问题整体解的存在性 .     

一类具积分项非线性梁方程整体解的存在性

讨论了一类在轴向载荷作用下,有限长粘弹性梁的非线性振动问题,用Galerkin方法证明了问题的整体强解和整体经典解的存在性.     

非线性Boltzmann-Poisson方程组的整体光滑解

本文研究双极半导体器件的古典Ｂｏｌｔｚｍａｎｎ－Ｐｏｉｓｓｏｎ模型,在考虑碰撞及产生复合项的条件下, 证明了其Ｃａｕｃｈｙ问题的整体光滑解的存在唯一性．     

非线性Boltzmann-Poisson方程组的整体光滑解

本文研究双极半导体器件的古典Boltzmann-Poisson模型, 在考虑碰撞及产生复合项的条件下, 证明了其Cauchy问题的整体光滑解的存在唯一性.     

具有奇性的常微分方程的边值问题

本文对具有奇性的常微分方程的边值问题（ｔ）ｙ'=(ｔ，ｙ，ｙ＇），ｙ（０）＝ａ，ｙ（１）＝ｂ建立了Ｎａｇｕｍｏ型存在定理．     

Formation of Singularities of Solutions for Cauchy Problem of Quasilinear Hyperbolic Systems with Dissipative Terms

ln this paper, for a class of 2 × 2 quasilinear hyperbolic systems, we get existence theorems of the global smooth solutions of its Cauchy problem, under a certain hypotheses. In addition, Tor two concrete quasilinear hyperbolic systems, we study the formation of the singularities of the C¹-solution to its Cauchy problem.     

一类拟线性波方程的整体光滑解

In this paper, we study the Cauchy problem for the following quasi-linear wave equation utt-2kuxxtt=β(uxn)x, where k>0 and βare real numbers, and n≥2 is an integer. We prove that for any T>0, the Cauchy problem admits a unique global smooth solution u ∈C∞((0, T); H∞(R))∩C ([0, T]; H2(R))∩C1([0, T]; L2(R)) under suitable assumptions on the initial data.     

Formation of Singularities for Quasilinear Hyperbolic Systems with Characteristics with Constant Multiplicity

In this paper we consider the Cauchy problem for quasilinear hyperbolic systems with characteristics with constant multiplicity. Without restriction on characteristics with constant multiplicity(> 1), under the assumptions that there is a genuinely nonlinear simple characteristic and the initial data possess certain decaying properties, the blow-up result is obtained for the C¹ solution to the Cauchy problem.     

一维Navier-Stokes方程组整体经典解

本文作者考虑了一维Navier-Stokes方程组Cauchy问题,得到了其经典解的整体光滑可解性。     

Global Smooth Solutions to a System of Dissipative Nonlinear Evolution Equations

The existence and uniqueness are proved for global classical solutions of the following initial-boundary problem for the system of parabolic equations which is proposed by Hsieh as a substitute for the Rayleigh-Benard equation and can lead to Lorenz equations: {ψ_t = -(σ - α)ψ - σθ_x, + αψ_{xx} θ_t = -(1- β)θ + vψ_x + (ψθ)_x + βθ_{xx} ψ(0,t) = ψ(1,t) = 0, θ_x(0,t) = θ_x(1,t) = 0 ψ(x,0) = ψ_0(x), θ(x,0) = θ_0(x)     

Global well‐posedness of classical solutions to 3D compressible magnetohydrodynamic equations with large potential force

We consider the Cauchy problem of isentropic compressible magnetohydrodynamic equations with large potential force in . When the initial data (ρ₀,u₀,H₀) is of small energy, we investigate the global well‐posedness of classical solutions where the flow density is allowed to contain vacuum states.     

Global Existence of Solutions for the Cauchy Problem of the Kawahara Equation with L 2 Initial Data

In this paper we study solvability of the Cauchy problem of the Kawahara equation 偏导dtu ＋ au偏导dzu ＋ β偏导d^3xu ＋γ偏导d^5xu = 0 with L^2 initial data. By working on the Bourgain space X^r,s（R^2） associated with this equation, we prove that the Cauchy problem of the Kawahara equation is locally solvable if initial data belong to H^r（R） and -1 〈 r ≤ 0. This result combined with the energy conservation law of the Kawahara equation yields that global solutions exist if initial data belong to L^2（R）.     

具张弛的拟线性双曲守恒律方程组

In this paper,we investigate the relaxation phenomenon for quasilinear hyper- bolic conservation laws,and obtain global smooth solutions and the life span of classical solutions to its Canchy problem.These results shows that the relaxation admits the effects of dissipation.     

Global existence of classical solutions to two‐dimensional Navier–Stokes equations with Cauchy data containing vacuum

In this paper, the Cauchy problem to the two‐dimensional isentropic compressible Navier–Stokes equations with smooth initial data containing vacuum is investigated. If the initial data are of small energy but possibly large oscillations, we obtain the global well‐posedness of classical solutions in the case of initially nonvacuum far fields. In particular, the smallness of the energy only depends on the norm of the initial velocity, where β can be arbitrary close to 0. In the case of compactly supported initial density, a blow‐up example is given. Copyright © 2013 John Wiley & Sons, Ltd.