共查询到20条相似文献,搜索用时 15 毫秒
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First-passage failure of a classical business cycle model subject to time-delayed feedback control and wide-band random excitation is investigated in this paper. First, we get the averaged equation by using a stochastic averaging method, and then a backward Kolmogorov equation governing the conditional reliability function and a set of generalized Pontryagin equations governing the conditional moments of first-passage time are established. The conditional reliability function, the conditional probability density and moments of first-passage time are obtained by solving the backward Kolmogorov equation and generalized Pontryagin equations analytically and numerically with suitable initial and boundary conditions. The results show that time delay in the feedback control forces may remarkably reduce the conditional reliability and the mean first-passage time of the controlled economics system. 相似文献
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The functionally generalized variable separation solutions of a general KdV-type equations ut=uxxx + A(u, ux)uxx + B(u, ux) are investigated by developing the conditional Lie-Bäcklund symmetry method. A complete classification of the considered equations, which admit multi-dimensional invariant subspaces governed by higher-order conditional Lie-Bäcklund symmetries, is presented. As a result, several concrete examples are provided to construct functionally generalized variable separation solutions of some resulting equations. 相似文献
4.
Changzheng Qu 《International Journal of Theoretical Physics》1996,35(12):2679-2685
New exact solutions toN-dimensional radially symmetric nonlinear diffusion equations with power-law diffusivities are constructed in terms of the generalized conditional symmetry method, which can be thought as a generalization of the nonclassical symmetry method due to Bluman and Cole. 相似文献
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Conditional Symmetry Groups of Nonlinear Diffusion Equations with x-Dependent Convection and Absorption 总被引:1,自引:0,他引:1
The generalized
conditional symmetry and sign-invariant approaches are developed
to study the nonlinear diffusion equations with x-dependent
convection and source terms. We obtain conditions under which the
equations admit the second-order generalized conditional
symmetries and the first-order sign-invariants on the solutions.
Several types of different generalized conditional symmetries and
first-order sign-invariants for the equations with diffusion of
power law are obtained. Exact
solutions to the resulting equations are constructed. 相似文献
6.
Using the generalized conditional symmetry approach, we obtain a
number of new generalized
(1+1)-dimensional nonlinear wave
equations that admit derivative-dependent functional separable
solutions. 相似文献
7.
The functionally generalized variable separation of the generalized nonlinear diffusion equations ut = A(u, ux)uxx +B(u, ux) is studied by using the conditional Lie–Ba¨cklund symmetry method. The variant forms of the considered equations,which admit the corresponding conditional Lie–Ba¨cklund symmetries, are characterized. To construct functionally generalized separable solutions, several concrete examples defined on the exponential and trigonometric invariant subspaces are provided. 相似文献
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Using the generalized conditional symmetry approach, a complete list of canonicalforms for the Kortewegde-Vries type equations with which possessing derivative-dependent functional separable solutions (DDFSSs) is obtained.The exact DDFSSs of the resulting equations are explicitly exhibited. 相似文献
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ZHANG Shun-Li WANG Yong LOU Sen-Yue 《理论物理通讯》2007,47(6):975-980
The concept of approximate generalized conditional symmetry (AGCS) for the perturbed evolution equations is introduced, and how to derive approximate conditional invariant solutions to the perturbed equations via their A GCSs is illustrated with examples. 相似文献
10.
We exploit higher-order conditional symmetry to reduce initial-value problems for evolution equations to Cauchy problems for systems of ordinary differential equations (ODEs). We classify a class of fourth-order evolution equations which admit certain
higher-order generalized conditional symmetries (GCSs) and give some examples to show the main reduction procedure. These reductions cannot be derived within the framework of the standard Lie approach, which hints that the technique presented here is
something essential for the dimensional reduction of evolution equations. 相似文献
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This paper is devoted to the study of functional variable separation for extended nonlinear elliptic equations.By applying the functional variable separation approach to extended nonlinear elliptic equations via the generalized conditional symmetry, we obtain complete classification of those equations which admit functional separable solutions (FSSs) and construct some exact FSSs to the resulting equations. 相似文献
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The functionally separable solutions of the generalized inhomogeneous nonlinear diffusion equations are studied by applying the conditional Lie–Bäcklund symmetry method. A complete list of canonical forms for such equations are presented. Exact solutions to the resulting equations are constructed. The asymptotic behaviors and blow-up properties of some solutions are also discussed. 相似文献
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The generalized conditional symmetry approach is applied to study the variable separation of the extended wave equations. Complete classification of those equations admitting functional separable solutions is obtained and exact separable solutions to some of the resulting equations are constructed. 相似文献
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Classification and Functional Separable Solutions to Extended Nonlinear Wave Equations 总被引:1,自引:0,他引:1
ZHANG Shun-Li LOU Sen-Yue QU Chang-Zheng YUE Rui-Hong 《理论物理通讯》2005,44(4):589-596
The generalized conditional symmetry approach is applied to study the variable separation of the extended wave equations. Complete classification of those equations admitting functional separable solutions is obtained and exact separable solutions to some of the resulting equations are constructed. 相似文献
15.
ZHANG Shun-Li 《理论物理通讯》2006,45(6):969-978
The generalized conditional symmetry is developed to study the variable
separation for equations of type uxt=A(u,ux)uxx+B(u,ux). Complete classification of those equations which admit derivative-dependent functional separable solutions is obtained and some of their
exact separable solutions are constructed. 相似文献
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Symmetry reduction of a class of third-order evolution equations that admit certain generalized conditional symmetries (GCSs) is implemented. The reducibility of the initial-value problem for an evolution equation to a Cauchy problem for a system ofordinary differential equations (ODEs) is characterized via the GCS and its Lie symmetry. Complete classification theorems are obtained and some examples are taken to show the main reduction procedure. 相似文献
18.
This paper is devoted to studying symmetry reduction of Cauchy problems for the fourth-order quasi-linear parabolic equations that admit certain generalized conditional symmetries (GCSs). Complete group classification results are presented, and some examples are given to show the main reduction procedure. 相似文献
19.
JI Li-Na QU Chang-Zheng 《理论物理通讯》2006,46(10)
The present paper discusses a class of nonlinear diffusion-convection equations with source. The method that we use is the conditional symmetry method. It is shown that the equation admits certain conditional symmetries for coefficient functions of the equations. As a consequence, solutions to the resulting equations are obtained. 相似文献
20.
Conditional Symmetries and Solutions to a Class of Nonlinear Diffusion-Convection Equations 总被引:1,自引:0,他引:1
JI Li-Na QU Chang-Zheng 《理论物理通讯》2006,46(4):668-674
The present paper discusses a class of nonlinear diffusion-convection equations with source. The method that we use is the conditional symmetry method. It is shown that the equation admits certain conditional symmetries for coefficient functions of the equations. As a consequence, solutions to the resulting equations are obtained. 相似文献