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1.
本文只用一个纵波信息,对一维波动方程的速度和震源函数进行联合反演.并考虑到波动方程的反问题是一不适定问题,对震源函数和波速分别用正则化法分步迭代求解,大大减少了反问题的计算工作量,改善了该反问题的计算稳定性.为计算实际一维地震数据提供了一种方法.文中给出了只用一个反问题补充条件同时进行多参数反演的详细公式,并对相应的数值算例进行了分析和比较. 相似文献
2.
Jong Uhn Kim 《Applied Mathematics and Optimization》2006,54(2):237-261
We discuss the Cauchy problem for a one-dimensional wave equation with white noise boundary condition. We also establish
the existence of an invariant measure when the noise is additive. Similar problems for parabolic equations were discussed
by several authors. To our knowledge, there is only one work [12] which investigated the initial-boundary value problem for
a wave equation with random noise at the boundary. We handle a more general case by a different method. Our result on the
existence of an invariant measure relies on the author's recent work on a certain class of stochastic evolution equations. 相似文献
3.
We consider the point vortex model associated to the modified Surface Quasi-Geostrophic(mSQG) equations on the two dimensional torus. It is known that this model is well posed for almost every initial conditions. We show that, when the system is perturbed by a certain space-dependent noise, it admits a unique global solution for any initial configuration. We also present an explicit example for the deterministic system on the plane where three different point vortices collapse. 相似文献
4.
We consider a quasilinear equation that consists of the inviscid Burgers equation plus O(α2) nonlinear terms. As we show, these extra terms regularize the Burgers equation in the following sense: for smooth initial
data, the α > 0 equation has classical solutions globally in time. Furthermore, in the zero-α limit, solutions of the regularized
equation converge strongly to weak solutions of the Burgers equation. We present numerical evidence that the zero-α limit
satisfies the Oleinik entropy inequality. For all α ≥ 0, the regularized equation possesses a nonlocal Poisson structure.
We prove the Jacobi identity for this generalized Hamiltonian structure. 相似文献
5.
Y. Fujita 《Applied Mathematics and Optimization》2001,43(2):169-186
In this paper we consider the Bellman equation in a one-dimensional ergodic control. Our aim is to show the existence and
the uniqueness of its solution under general assumptions. For this purpose we introduce an auxiliary equation whose solution
gives the invariant measure of the diffusion corresponding to an optimal control. Using this solution, we construct a solution
to the Bellman equation. Our method of using this auxiliary equation has two advantages in the one-dimensional case. First,
we can solve the Bellman equation under general assumptions. Second, this auxiliary equation gives an optimal Markov control
explicitly in many examples. \keywords{Bellman equation, Auxiliary equation, Ergodic control.}
\amsclass{49L20, 35G20, 93E20.}
Accepted 11 September 2000. Online publication 16 January 2001. 相似文献
6.
Ukrainian Mathematical Journal - We solve a selection problem for multidimensional SDE dX(t) = a(X??(t)) dt + ??σ(X??(t)) dW(t), where the drift and... 相似文献
7.
Ukrainian Mathematical Journal - We prove the existence of a sticky-reflected solution to the heat equation on the space interval [0, 1] driven by colored noise. The process can be interpreted as... 相似文献
8.
考虑了标准的一维逆热传导方程.问题是不适定的,即解不连续地依赖于数据.通过Fourier逼近的方法进行正则化处理,提出了一个新的算法,理论分析和数值实验均表明该算法是稳定的;该算法不仅保留了测量数据的部分高频成份,同时还具有相同的精度和计算复杂性. 相似文献
9.
10.
M. L. Maslakov 《Computational Mathematics and Mathematical Physics》2018,58(4):529-536
This paper examines the solution of convolution-type integral equations of the first kind by applying the Tikhonov regularization method with two-parameter stabilizing functions. The class of stabilizing functions is expanded in order to improve the accuracy of the resulting solution. The features of the problem formulation for identification and adaptive signal correction are described. A method for choosing regularization parameters in problems of identification and adaptive signal correction is suggested. 相似文献
11.
12.
Summary. The dynamical behavior of the damped sine-Gordon equation with homogeneous Neumann boundary condition is studied. It is shown that the equation has an unbounded one-dimensional global attractor in a suitable functional space when the ``damping' and the ``diffusing' are not very small. Received March 16, 1999; accepted December 10, 1999 相似文献
13.
In this work, some classes of initial boundary-value problems are investigated in the Sobolev space for the third-order linear pseudoparabolic equation having, in general, nonsmooth coefficients. A new type of Riemann function concept is given for these problems, which is more natural than the classical Riemann-type function concept, and an integral form of the solutions of nonhomogeneous problems can be found more naturally using this concept. 相似文献
14.
一维对流扩散方程CRANK—NICOLSON特征差分格式 总被引:10,自引:0,他引:10
本文针对一维线性和非线性对流扩散方程提出一种Crank-Nicolson类型的特征差分格式,给出了该格式形成的线性代数方程组可解的一个充条件,证明了该格式按离散L^2模是收敛的,且其收敛阶为O(△t^ h^2). 相似文献
15.
In this paper we study a class of parabolic equations with a nonlinear gradient term. The system is disturbed by white noise in time. We show that the unique solution of this problem can be represented as the Wick product between a normalized random variable of exponential form and the solution of a nonlinear parabolic equation. We allow random initial data which might be anticipating. A relation between the Wick product with a normalized exponential and translation is proved in order to establish our results. 相似文献
16.
本文在半空间中研究一般的一维滤流方程的第三边值问题.这个问题描述了土壤中有非线性扩散、对流(蒸发)和吸收相互作用而且地表有供水或抽水时地下水的运动.我们证明了唯一弱解的存在性,这个弱解可以用单调不增的正解序列来逼近,在初值有正下界的情况下,我们证明了古典解局部存在性. 相似文献
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18.
Potential Analysis - We prove absolute continuity of the law of the solution, evaluated at fixed points in time and space, to a parabolic dissipative stochastic PDE on L2(G), where G is an open... 相似文献
19.
The problem of determining the kernel h(t), t ∈ [0, T], appearing in the system of integro-differential thermoviscoelasticity equations is considered. It is assumed that the coefficients of the equations depend only on one space variable. The inverse problem is replaced by the equivalent system of integral equations for unknown functions. The contraction mapping principle with weighted norms is applied to this system in the space of continuous functions. A global unique solvability theorem is proved and an estimate of the stability of the solution of the inverse problem is obtained. 相似文献
20.
本文通过一端固定 ,一端 Dirichlet边界控制的一维波动方程说明系统是 Salamon- W eiss意义下适定和正则的 .由此说明 ,由 J.L.Lions引入的用于研究双曲方程精确可控性的 H ilbert唯一性方法是控制论中著名的对偶原理 .我们讨论了系统的指数镇定及闭环系统的广义本征函数生成 Riesz基和谱确定增长条件 .我们希望通过本文使读者对目前线性偏微分控制理论的一个新动向有一基本的了解 . 相似文献