In the present paper we first obtain the comparison principle for the nonlinear stochastic differentialdelay equations with Markovian switching. Later, using this comparison principle, we obtain some stabilitycriteria...In the present paper we first obtain the comparison principle for the nonlinear stochastic differentialdelay equations with Markovian switching. Later, using this comparison principle, we obtain some stabilitycriteria, including stability in probability, asymptotic stability in probability, stability in the pth mean, asymptoticstability in the pth mean and the pth moment exponential stability of such equations. Finally, an example isgiven to illustrate the effectiveness of our results.展开更多
In this paper, we study the existence and uniqueness of solutions to stochastic differential equations driven by G-Brownian motion （GSDEs） with integral-Lipschitz coefficients.
In this paper, we study the property of continuous dependence on the parameters of stochastic integrals and solutions of stochastic differential equations driven by the G-Brownian motion. In addition, the uniqueness a...In this paper, we study the property of continuous dependence on the parameters of stochastic integrals and solutions of stochastic differential equations driven by the G-Brownian motion. In addition, the uniqueness and comparison theorems for those stochastic differential equations with non-Lipschitz coefficients are obtained.展开更多
A set of nonlinear partial differential equations was used to describe the motions of an internal flowing system, with the consideration of transient fluid structure interaction (FSI). The stability characteristics of...A set of nonlinear partial differential equations was used to describe the motions of an internal flowing system, with the consideration of transient fluid structure interaction (FSI). The stability characteristics of the system were analyzed on the basis of the nonlinear FSI-equation model. The results show that the stability of the nonlinear FSI system become very complicated because of the influence of strongly coupled interaction between flowing liquid and vibrating pipe. The flowing velocity, pressure, the piping stiffness, and constrained conditions, etc. play a very important role in developing procedure of the system stabilization. In an analysis example given in this paper, for example, when the flowing pressure is comparatively small, the system exhibits flutter instability, and when the flowing pressure is increases to a specified value, a subcritical divergence and a supercritical flutter bifurcation take successively place in the same velocity range.展开更多
In this note, we study a discrete time approximation for the solution of a class of delayed stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H ∈(1/2,1). In order to prove ...In this note, we study a discrete time approximation for the solution of a class of delayed stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H ∈(1/2,1). In order to prove convergence, we use rough paths techniques. Theoretical bounds are established and numerical simulations are displayed.展开更多
The fundamental equations of multiphase flow that have been established so far fall into two main groups, the multifluid model and the mixture model [1] [2]. Because of the different forms of the equations derived fro...The fundamental equations of multiphase flow that have been established so far fall into two main groups, the multifluid model and the mixture model [1] [2]. Because of the different forms of the equations derived from these two models, many disputes arose [1] [3] [4]. This paper deals mainly with the basic principles for establishing the fundamental equations of multiphase flow, namely the principles of consistency, invariance of material coordinates and material indifference. The results lead to the consistent description of the two models.展开更多
基金This work was supported by the National Natural Science Foundation of China (Grant No. 10171009) Tianyuan Young Fund of China (Grant No. 10226009).
文摘In the present paper we first obtain the comparison principle for the nonlinear stochastic differentialdelay equations with Markovian switching. Later, using this comparison principle, we obtain some stabilitycriteria, including stability in probability, asymptotic stability in probability, stability in the pth mean, asymptoticstability in the pth mean and the pth moment exponential stability of such equations. Finally, an example isgiven to illustrate the effectiveness of our results.
基金supported by the Major Program in Key Research Institute of Humanities and Social Sciences sponsored by Ministry of Education of China(under grant No.2009JJD790049)the Post-graduate Study Abroad Program sponsored by China Scholarship Council
文摘In this paper, we study the existence and uniqueness of solutions to stochastic differential equations driven by G-Brownian motion （GSDEs） with integral-Lipschitz coefficients.
文摘In this paper, we study the property of continuous dependence on the parameters of stochastic integrals and solutions of stochastic differential equations driven by the G-Brownian motion. In addition, the uniqueness and comparison theorems for those stochastic differential equations with non-Lipschitz coefficients are obtained.
基金TheworkwassupportedbytheNationalNaturalScienceFoundationofChina (No :5 0 0 790 0 7) thekeyprojectofScienceandTechnolgyinHydraulicEngineeringfromtheMinistryofWaterConservancy (No :Sz9830 )andtheProvincialNaturalScienceFoundationofYunnan (No :97E0 0
文摘A set of nonlinear partial differential equations was used to describe the motions of an internal flowing system, with the consideration of transient fluid structure interaction (FSI). The stability characteristics of the system were analyzed on the basis of the nonlinear FSI-equation model. The results show that the stability of the nonlinear FSI system become very complicated because of the influence of strongly coupled interaction between flowing liquid and vibrating pipe. The flowing velocity, pressure, the piping stiffness, and constrained conditions, etc. play a very important role in developing procedure of the system stabilization. In an analysis example given in this paper, for example, when the flowing pressure is comparatively small, the system exhibits flutter instability, and when the flowing pressure is increases to a specified value, a subcritical divergence and a supercritical flutter bifurcation take successively place in the same velocity range.
基金supported by MATH-AmSud 18-MATH-07 SaS MoTiDep ProjectHERMES project 41305+1 种基金partially supported by the Project ECOS-CONICYT C15E05,REDES 150038,MATH-AmSud 18-MATH-07 SaS MoTiDep Project and Fondecyt(1171335)supported by NSF(Grant DMS-1613163)
文摘In this note, we study a discrete time approximation for the solution of a class of delayed stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H ∈(1/2,1). In order to prove convergence, we use rough paths techniques. Theoretical bounds are established and numerical simulations are displayed.
文摘The fundamental equations of multiphase flow that have been established so far fall into two main groups, the multifluid model and the mixture model [1] [2]. Because of the different forms of the equations derived from these two models, many disputes arose [1] [3] [4]. This paper deals mainly with the basic principles for establishing the fundamental equations of multiphase flow, namely the principles of consistency, invariance of material coordinates and material indifference. The results lead to the consistent description of the two models.
