半线性SCHR(O)DINGER方程初值问题的L2-适定性

在RN(N≥2)中讨论一类具时间依赖系数的半线性Schr(o)dinger方程初值问题的L2-适定性.在Lorentz空间中,通过Strichartz估计和解的先验估计,得到了系数零点阶数λ与临界适定指数σ之间的关系,在一定条件下证明了问题的L2-整体适定性.     

半线性Schrdinger方程初值问题的H~1-适定性

在RN(N≥2)中讨论一类具时间依赖系数的半线性Schrdinger方程初值问题的H1-适定性.通过Strichartz估计和解的先验估计,得到了系数零点阶数λ与临界适定指数σ之间的关系,在一定条件下证明了该问题的H1-局部适定性和整体适定性.     

半线性Schr(o)dinger方程初值问题的H1-适定性

在RN(N≥2)中讨论一类具时间依赖系数的半线性Schr(o)dinger方程初值问题的H1-适定性.通过Strichartz估计和解的先验估计,得到了系数零点阶数λ与临界适定指数σ之间的关系,在一定条件下证明了该问题的H1-局部适定性和整体适定性.     

半线性Schroinger方程初值问题的H^-定性

在R^N（N≥2）中讨论一类具时间依赖系数的半线性SchroSdinger方程初值问题的H^1一适定性．通过Strichartz估计和解的先验估计，得到了系数零点阶数λ与临界适定指数σ之间的关系，在一定条件下证明了该问题的H^1-局部适定性和整体适定性．     

一类半线性波动方程的适定性

该文研究了一类带有效时变阻尼与变质量项的半线性波动方程弱解的整体存在性和有限时刻爆破现象.当非线性项指数p> pF(N)=1+2/N时,证明了在指数加权能量空间中,此问题的小初值的解整体存在;而当1F(α,n)=1+2(1+α)/N(1+α)-2α(0<α<1)时,对于一些方程中特定的参数和满足积分符号条件的初值,证明了此问题的解必在有限时间内爆破.     

A STRUCTURE-PRESERVING DISCRETIZATION OFNONLINEAR SCHRDINGER EQUATION

1.IntroductionManyimportantdifferentialequationsofevolutiontypeinphysicsandmechanicshavespecificgeometricstructure.Forinstance,theHamiltoniansystemsinclassicalmechanics,theSchrodingerequationinquantum,theKorteweg-deVriesandKleinGordonequationsofnonli...     

A REPRESENTATION FORMULA RELATED TO SCHRDINGER OPERATORS

Schrdinger operator is a central subject in the mathematical study of quanturn mechanics.Consider the Schrodinger operator H=-△+Ⅴ on R,where △=d2/dx2 and the potentialfunction Ⅴ is real valued.In Fourier analysis.it is well—known that a square integrable functionadmits an expansion with exponentials as eigenfunctions of—△.A natural Conjecture is that anL2 function admits a similar expansion in terms of“eigenfunctions”of H,a perturbation of theLaplacian(see [7],Ch.Ⅺ and the notes),under certain condition on Ⅴ.     

非静力旋转流体方程初值问题的适定性

应用分层理论所提供的方法,通过对非静力旋转流体方程这个数学模型本身的拓扑性质进行系统的理论分析和研究,来讨论对于这个方程的初值问题的几种不同提法以及相应的适定性问题．     

一类广义层流方程初值问题的整体适定性

讨论了刻画层流问题中比重相近的层间相互作用的数学模型的初值问题.通过引进一类函数空间并证明该初值问题的解在所述空间上的一系列先验估计,得到了该初值问题在初值属于Hs(R)(s≥1)时的整体适定性.     

THE INVARIANT MANIFOLDS FOR A PERTURBED QUINTIC-CUBIC SCHRDINGER EQUATION

In this paper, the authors apply the analytical method to establish the persistence of invariant manifolds for certain perturbation of the quintic-cubic Schrodinger equation under even periodic boundary conditions.     

半线性波动方程振荡初值问题的能量密度

利用微局部亏损测度研究了具有振荡初值的半线性波动方程的能量密度并解决了非线性几何光学领域中的一个问题。     

ON INITIAL BOUNDARY VALUE PROBLEMS FOR NONLINEAR SCHRDINGER EQUATIONS

ＯＮＩＮＩＴＩＡＬ　ＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＳＦＯＲＮＯＮＬＩＮＥＡＲＳＣＨＲＤＩＮＧＥＲＥＱＵＡＴＩＯＮＳ￥ＬｉＹｏｎｇｓｈｅｎｇ（李用声）ＣｈｅｎＱｉｎｇｙｉ（陈庆益）（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＨｕａｚｈｏｎｇＵｎｖ．ｏｆＳｃｉ...     

高阶非线性Schrdinger方程的整体适定性

本文研究了一类非线性高阶Schrdinger方程Cauchy问题的整体适定性.利用不动点定理,获得了整体解的存在唯一性及解关于初值的连续依赖性和解具有较强的衰减估计.推广了文献[4]中的结果.     

EXACT BOUNDARY CONTROLLABILITY OF 1-D NONLINEAR SCHRDINGER EQUATION

In this paper,the boundary control problem of a distributed parameter system described by the Schrdinger equation posed on finite intervalα≤x≤β: iyt yxx |y|~2y=0, y(α,t)=h_`1(t),y(β,t)=h_2(t)for t>0(S) is considered.It is shown that by choosing appropriate control inputs(h_j),(j=1,2)one can always guide the system(S)from a given initial stateφ∈H~s(α,β),(s∈R)to a terminal stateΨ∈H~s(α,β),in the time period[0,T].The exact boundary controllability is obtained by considering a related initial value control problem of Schrdinger equation posed on the whole line R.The discovered smoothing properties of Schrdinger equation have played important roles in our approach;this may be the first step to prove the results on boundary controllability of(semi-linear)nonlinear Schrdinger equation.     

HARNACK’S INEQUALITY FOR GENERALIZED SUBELLIPTIC SCHRDINGER OPERATORS

We prove a uniform Harnack inequality for nonnegative solutions of ΔGu Gμu = 0, where ΔG is a sublaplacian, μ is a non-negative Radon measure and satisfying scale-invariant Kato condition.     

AREA FUNCTIONS ON HARDY SPACES ASSOCIATED TO SCHRDINGER OPERATORS

In this paper, the author gives a characterization of atomic Hardy spaces associated to Schrodinger operators by using area functions, and hence gets the dual spaces of atomic Hardy spaces.     

EXPLICIT DISSIPATIVE SCHEMES FOR BOUNDARY PROBLEMS OF GENERALIZED SCHRDINGER SYSTEMS

In this paper, the author constructs a class of explicit schemes, spanning two time levels, forthe initial--boundary-value problems of generalized nonlinear Schrodinger systems, and proves theconvergence of these schemes with a series of prior estimates. For a single Schrodinger equation, theschemes are identical with those of the article [1].     

SOME TRACE FORMULAS FOR THE SCHRDINGER EQUATION WITH ENERGY-DEPENDENT POTENTIAL

The importance of the inverse scattering problem for the Schrdinger equation with energy-dependent potential:     

NODAL BOUND STATES WITH CLUSTERED SPIKES FOR NONLINEAR SCHRDINGER EQUATIONS

We consider the following nonlinear Schr¨odinger equations -ε2△u + u = Q(x)|u|p-2u in RN, u ∈ H1(RN),where ε is a small positive parameter, N ≥ 2, 2 p ∞ for N = 2 and 2 p 2N/N-2 for N ≥ 3. We prove that this problem has sign-changing(nodal) semi-classical bound states with clustered spikes for sufficiently small ε under some additional conditions on Q(x).Moreover, the number of this type of solutions will go to infinity as ε→ 0+.     

抽象半线性发展方程初值问题的整体解

在抽象空间框架下,研究了具有广泛物理背景的一类半线性发展方程初值问题整体解的存在性。利用正算子半群特征与凸锥理论,把上下解方法引入该问题,给出了整体解存在及唯一的若干充分条件。所得的结果概括、统一及推广了常微分方程、偏微分方程及Banach空间常微分方程中的有关结论。