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对初值的连续依赖性
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  continuous dependence on initial value
     The Euler scheme for stochastic differential equations is first brought forward,then the Euler scheme with variable step-length for stochastic differential equations is presented,and their convergence and continuous dependence on initial value are discussed.
     首先给出了线性随机微分方程的欧拉格式算法,然后给出了非线性随机微分方程变步长的欧拉格式算法,接着讨论了其对初值的连续依赖性和收敛性.
短句来源
  “对初值的连续依赖性”译为未确定词的双语例句
     W_(tt)-[a0 +a_1 (W_x)~(2m)]W_(xx)-λW_(xx)=0 a_0~>0, a_1≥0, λ≥0 in the rec- tangular demain[0, π]x[o, t] and proved the asymptotic behavior of the solution of the equation when λ→0.
     Wtt—[a_0+a_1(Wx)~2]Wxx—λ Wxxt=0,a_0>0,a_1≥0,λ≥0。 在矩形域[0,π]×[0,t]上的角的存在性,唯一性及解对初值的连续依赖性,并且讨论了当λ→0时解的渐近性态。
短句来源
     This paper is concerned with the global existence, uniqueness of H2generalized solutions and continuous dependence on the initial data of Higeneralized global solutions (i=1,2) to the initial boundary value problem with the Dirichlet boundary conditions for the compressible NavierStokes equations of a onedimensional viscous polytropic ideal gas for large initial data.
     研究具有Dirichlet边界条件和"大"初值的一维粘性多方理想气体可压缩Navier-Stokes方程组的初边值问题H2广义解的整体存在性、唯一性及Hi(i=1,2)广义解对初值的连续依赖性.
短句来源
     Discussions on the Continuous Dependence Theorem of Solution to Starting Values
     有关解对初值的连续依赖性定理的探讨
短句来源
     Also in the second part, with analyzing the properties of an operator , the globalexistence and uniqueness, the regularity and the dependence on the initial valuesof the solution about this model are presented.
     论文的第二部分是具体解一个非局部的非线性偏微分模型,同样运用了算子不动点方法讨论了模型的适定性,并进一步得到解对初值的连续依赖性即稳定性。
短句来源
     At first,we proved the existence and uniqueness of the positive local solution of the problem by using the implicit function system theorem.
     首先,利用隐函数定理证明了该问题的局部解的存在性与唯一性,以及解对初值的连续依赖性.
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  相似匹配句对
     Discussions on the Continuous Dependence Theorem of Solution to Starting Values
     有关解初值连续依赖性定理探讨
短句来源
     The continuity and continuous dependence on initial values of the solution are proved.
     证明了解连续性及解初值连续依赖性.
短句来源
     Continuous dependence of the solutions on initial condition and parameter for a nonautonomous differential equation
     一类非自治微分方程解初值和参数连续依赖性
短句来源
     Continuous Dependence on the Initial-time Geometry for Forward Heat Equation with Different Prescribed Data
     具有不同初值前向热方程初始时刻几何连续依赖性
短句来源
     Continuous Dependence on the Initial-time Geometry for the Heat Equation With Different Initial Data
     具有不同初值倒向热方程初始时刻几何连续依赖性
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In this paper, we consider the quasilincar differential-difference equation of advanced type cf the formwhere A0, B0 are NxN constant matrices. x(t) is N-column vectors function, f(t, x(t), x(t + r)) is continuous function from some subset of [to, +∞)×(RN) 2 in to RN. We have proved that if linear equation with constant coefficientsexists the bounded solution u(t) andthen the equation (*) exists bounded solution under certain condition.For scalar equation (*) , we have proved that Uniqueness of bounded solution,...

In this paper, we consider the quasilincar differential-difference equation of advanced type cf the formwhere A0, B0 are NxN constant matrices. x(t) is N-column vectors function, f(t, x(t), x(t + r)) is continuous function from some subset of [to, +∞)×(RN) 2 in to RN. We have proved that if linear equation with constant coefficientsexists the bounded solution u(t) andthen the equation (*) exists bounded solution under certain condition.For scalar equation (*) , we have proved that Uniqueness of bounded solution, dependence of bounded solution on initial condition and asymptotic behavior of bounded solution.

本文考虑超前型拟线性微分差分方程,得到了存在有界解的充分条件;对纯量方程还得到了保证有界解的唯一性及有界解对初值连续依赖性的充分条件,并给出了有界解的渐近式

We consider the nonlinear functional differential equation of advanced type form of (t)=F(t, x_t) and the initial condition x(t_0)=ξ where x_t(θ) =x(t+θ)∈C([0,+∞);R~n).In this paper, we give the sufficient condition for exists the bounded generalized solution, and proved that uniqueness theorem of bounded generalized solution; continuous dependence theorem of bounded generalized solution on initial value.

本文对超前型非线性泛函微分方程的初值问题得到了在t≥t_o上存在有界广义解的充分条件,并证明了解的唯一性与解对初值的连续依赖性,其中 x_i(θ)=x(t+θ)

In this paper,we built a variation-of-constants formula for functionaldifferential equation of advanced type form of(?)(t)=integral from 0 to ∞ d_θη(t,θ)x(t+θ)+F(t,x_t) (*)via an evolution system associated with the bounded generalized solution on[s,+∞) of linear functional differential equation of advanced type form of(?)(t)=integral from 0 to ∞[d_θη(t,θ)]x(t+θ)and initial conditionx(s)=ξ,and proved that the existence,uniqueness and continuous dependence of thebounded generalized solution of quasilinear equation(*)....

In this paper,we built a variation-of-constants formula for functionaldifferential equation of advanced type form of(?)(t)=integral from 0 to ∞ d_θη(t,θ)x(t+θ)+F(t,x_t) (*)via an evolution system associated with the bounded generalized solution on[s,+∞) of linear functional differential equation of advanced type form of(?)(t)=integral from 0 to ∞[d_θη(t,θ)]x(t+θ)and initial conditionx(s)=ξ,and proved that the existence,uniqueness and continuous dependence of thebounded generalized solution of quasilinear equation(*).

本文以发展系统为工具,对超前型拟线性泛函微分方程建立了常数变易公式,并用它证明拟线性方程有界广义解的存在性、唯一性与解对初值的连续依赖性.

 
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