Quantum Euler-Poisson System: Local Existence of Solutions

The one-dimensional transient quantum Euler-Poisson system for semiconductors is studied in a bounded interval. The quantum correction can be interpreted as a dispersive regularization of the classical hydrodynamic equations and mechanical effects. The existence and uniqueness of local-in-time solutions are proved with lower regularity and without the restriction on the smallness of velocity, where the pressure-density is general (can be non-convex or non-monotone).     

一类非线性m-点边值问题正解的存在性

设α∈C[0,1],b∈C([0,1],(-∞,0)).设φ(t)为线性边值问题 u″+a(t)u′+b(t)u=0, u′(0)=0,u(1)=1的唯一正解.本文研究非线性二阶常微分方程m-点边值问题 u″+a(t)u′+b(t)u+h(t)f(u)=0, u′(0)=0,u(1)-sum from i=1 to(m-2)((a_i)u(ξ_i))=0正解的存在性.其中ξ_i∈(0,1),a_i∈(0,∞)为满足∑_(i=1)~(m-2)a_iφ_1(ξ_i)<1的常数,i∈{1,…,m-2}.通过运用锥上的不动点定理,在f超线性增长或次线性增长的前提下证明了正解的存在性结果.     

具有吸收-反射边界的Boltzmann-Poisson输运模型的整体弱解

本文研究具有吸收-反射边界的Boltzmann-Poisson输运模型的初这值问题,并利用速度平均的稳定性和L~1空间紧致性理论,在较弱的初边值条件下,证明了其整体弱解的存在性。     

Monte carlo studies of phase transitions in polymer blends and block copolymer melts

Summary The unmixing transition of both symmetrical polymer blends AB (i.e. chain lengthsN _A=N _B=N) and asymmetrical ones (N _B/N _A=2,3) is studied by large-scale Monte Carlo simulations of the bond fluctuation model. Combination of semi-grand-canonical simulation techniques, ?histogram reweighting? and finitesize scaling allows an accurate location of the coexistence curve in the critical region. The variation of the critical temperature with chain length (N) is studied and compared to theoretical predictions. For the symmetrical case, use of chain lengths up toN=512 allows a rough estimation of crossover scaling functions for the crossover from Ising to mean-field exponents. The order-disorder transitions in melts of both symmetric (compositionf=N _A/(N _A+N _B)=1/2) and asymmetric (f=3/4) block copolymers is studied for very short chains (16≤N≤60). The interplay between structure and chain configuration is emphasized. Qualitative evidence for ?dumbell formation? of chains and vacancy enrichment in A-B-interfaces and near hard walls is presented. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

一类时滞Logistic差分方程的全局吸引性

§ 1　ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｉｄｅｒｔｈｅｎｏｎａｕｔｏｎｏｍｏｕｓｄｅｌａｙｌｏｇｉｓｔｉｃｄｉｆｆｅｒｅｎｃｅｅｑｕａｔｉｏｎΔｙｎ =ｐｎｙｎ( 1 - ｙτ(ｎ) )　 ,ｎ =0 ,1 ,2 ,...,( 1 1 )ｗｈｅｒｅｐｎ ∞ｎ =0 ｉｓａｓｅｑｕｅｎｃｅｏｆｐｏｓｉｔｉｖｅｒｅａｌｎｕｍｂｅｒｓ ,τ(ｎ) ∞ｎ =0 ｉｓａｎｏｎｄｅｃｒｅａｓｉｎｇｓｅｑｕｅｎｃｅｏｆｉｎｔｅｇｅｒｓ,τ(ｎ) <ｎａｎｄｌｉｍｎ→∞τ(ｎ) =∞ ,Δｙｎ=ｙｎ +1- ｙｎ.Ｍｏｔｉｖａｔｅｄｂｙｐｌａｕｓｉｂｌｅａｐｐｌｉｃａｔｉｏｎｓ…     

具有功能反应的两斑块扩散时滞竞争系统正周期解的存在性

§ 1　ＩｎｔｒｏｄｕｃｔｉｏｎＦｏｒｍａｎｙｓｐｅｃｉｅｓｔｈｅｓｐａｔｉａｌｆａｃｔｏｒｓａｒｅｉｍｐｏｒｔａｎｔｉｎｐｏｐｕｌａｔｉｏｎｄｙｎａｍｉｃｓ .Ｔｈｅｔｈｅｏｒｅｔｉｃａｌｓｔｕｄｙｏｆｓｐａｔｉａｌｄｉｓｔｒｉｂｕｔｉｏｎｈａｓｂｅｅｎｅｘｔｅｎｓｉｖｅｌｙｓｔｕｄｉｅｄｉｎｍａｎｙｐａｐｅｒｓ .Ｍｏｓｔｏｆｔｈｅｐｒｅｖｉｏｕｓｐａｐｅｒｓｆｏｃｕｓｅｄｏｎｔｈｅｃｏｅｘｉｓｔｅｎｃｅｏｆｐｏｐｕｌａｔｉｏｎｓｍｏｄｅｌｌｅｄｂｙｓｔｓｔｅｍｓｏｆｏｒｄｉｎａｒｙｄｉｆｆｅｒｅ…     

PARALLEL DYNAMIC ITERATION METHODS FOR SOLVING NONLINEAR TIME—PERIODIC DIFFERENTIAL—ALGEBRAIC EQUATIONS

In this paper we presented a convergence condition of paralle dynamic iteration meth-ods for a nonlinear system of differential-algebraic equations with a periodic constraint.The convergence criterion is decided by the spectral expressjon of a linear operator derived form system partitions.Numerical experiments given here confirm the theoretical work of the paper.     

Elliptic Equations with Degenerate Coercivity： Gradient Regularity

In this paper, we prove higher integrability results for the gradient of the solutions of some elliptic equations with degenerate coercivity whose prototype is where for example, a(x,u)=(1+|u|)^−θ with θ ∈ (0,1). We study the same problem for minima of functionals closely related to the previous equation.     

Invariant Tori and Boundedness in Asymmetric Oscillations

In this paper,we are concerned with the boundedness of all the solutions of the equation x″ ax^ -bx- Ф(x)=p(t),where p(t) is a smooth 2π-periodic function,a and b are positive constants,and the perturbation Ф(x) is bounded.     

Multidimensional transonic shocks and free boundary problems for nonlinear equations of mixed type

We establish the existence and stability of multidimensional transonic shocks for the Euler equations for steady potential compressible fluids. The Euler equations, consisting of the conservation law of mass and the Bernoulli law for the velocity, can be written as a second-order, nonlinear equation of mixed elliptic-hyperbolic type for the velocity potential. The transonic shock problem can be formulated into the following free boundary problem: The free boundary is the location of the transonic shock which divides the two regions of smooth flow, and the equation is hyperbolic in the upstream region where the smooth perturbed flow is supersonic. We develop a nonlinear approach to deal with such a free boundary problem in order to solve the transonic shock problem. Our results indicate that there exists a unique solution of the free boundary problem such that the equation is always elliptic in the downstream region and the free boundary is smooth, provided that the hyperbolic phase is close to a uniform flow. We prove that the free boundary is stable under the steady perturbation of the hyperbolic phase. We also establish the existence and stability of multidimensional transonic shocks near spherical or circular transonic shocks.