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针对Helmholtz方程Cauchy问题提出一种数值计算方法. 借助于DirichlettoNeumann映射, 将Cauchy问题转化为求解散射场初值的紧算子方程. 先讨论紧算子奇异值的渐近性质, 然后将投影法与Tikhonov正则化方法相结合, 提出一种求解相应紧算子方程的带有正则化技巧的投影法, 并通过数值实验验证了算法的有效性.
Abstract: The paper presents a reformulation of some of the most basic entities and equations of linear elasticity - the stress and strain tensor, the Cauchy Navier equilibrium equations, material equ...
A subset E of a metric space (X, d) is totally bounded if and only if any sequence of points in E has a Cauchy subsequence. We call a sequence (xn) statistically quasi-Cauchy if st − limn!1 d(xn...
In this survey we consider generalizations for Young and Cauchy–Bunyakowsky inequalities with applications.In section 2 it is noticed that in fact there two different Young inequalities (for two numbe...
In this paper, we study the Cauchy problem of a two-component b-family equation. We first establish the local well-posedness for a two-component b-family equation by Kato’s semigroup theory. Then, we ...
In this paper we expand the kernel of Cauchy integral equation of first kind as a series of Chebyshev polynomials of the second kind times some unknown functions. These unknown functions are determine...
Recently, M.K.-H. Kiessling and A.S. Tahvildar-Zadeh proved that a unique global classical solution to the relativistic Vlasov-Poisson system exists whenever the positive, integrable initial datum is...
Recently, the old notion of causal boundary for a spacetime V has been redefined in a consistent way. The computation of this boundary $\partial V$ for a standard conformally stationary spacetime V = ...
Recently, the old notion of causal boundary for a spacetime V has been rede ned in a consistent way. The computation of this boundary @V on any standard conformally stationary spacetime V = R  M, sug...
We consider the Cauchy problem for (energy-subcritical) nonlinear Schr¨odinger equations with sub-quadratic external potentials and an additional angular momentum rotation term. This equation is a wel...
Some known results regarding the Euler and Navier-Stokes equations were obtained by different authors.Existence and smoothness of the Navier-Stokes solutions in two dimensions have been known for a lo...
The geometric Cauchy problem for a class of surfaces in a pseudo-Riemannian manifold of dimension 3 is to find the surface which contains a given curve with a prescribed tangent bundle along the curve...
In this paper, we are interested in the Cauchy problem for the Boltzmann-BGK model for a general class of collision frequencies. We prove that the Boltzmann-BGK model linearized around a global Maxwel...
We consider the Cauchy problem for the nonlinear Schr¨odinger equation i@tu + u = 1u + 2|u| u in RN, in Hs subcritical case 0  < 4 N−2s , when 0 < s < N 2 and 0  < +1, when s > N 2 . We...
This paper is concerned with the analysis of the Cauchy problem of a general class of two-dimensional nonlinear nonlocal wave equations governing antiplane shear motions in nonlocal elasticity.

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