In this paper, we consider strong convergence and almost sure exponential stability of the backward Euler-Maruyama method for nonlinear hybrid stochastic differential equations with time-variable delay. Under the loca...
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In this paper, we consider strong convergence and almost sure exponential stability of the backward Euler-Maruyama method for nonlinear hybrid stochastic differential equations with time-variable delay. Under the local Lipschitz condition and polynomial growth condition, it is proved that the backward Euler-Maruyama method is strongly convergent. Additionally, the moment estimates and almost sure exponential stability for the analytical solution are proved. Also, under the appropriate condition, we show that the numerical solutions for the backward Euler-Maruyama methods are almost surely exponentially stable. A numerical experiment is given to illustrate the computational effectiveness and the theoretical results of the method.
Let A be an invertible d × d matrix with integer elements. Then A determines a self-map T of the d-dimensional torus Td = Rd/Zd. Given a real number τ > 0, and a sequence {zn} of points in Td, let Wτ be the ...
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Consider the eigenvalue problem of a linear second order elliptic operator: − D∆ − 2α∇m(x) · ∇ + V (x) = λ in Ω, complemented by the Dirichlet boundary condition or the following general Robin boundary conditi...
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In this paper, we consider asymptotic behavior of the principal eigenvalue of some second order elliptic operator with general boundary conditions. For $N=1$, we provide a complete characterization of the asymptotic b...
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In this paper, we study the homogenization of the distribution-dependent stochastic abstract fluid models by combining the two−scale convergence and martingale representative approach. A general framework of the homog...
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In this work, we consider the 3D Cauchy problem for a coupled system arising in biomathematics, consisting of a chemotaxis model with a cubic logistic source and the stochastic tamed Navier–Stokes equations (STCNS, f...
In this work, we consider the 3D Cauchy problem for a coupled system arising in biomathematics, consisting of a chemotaxis model with a cubic logistic source and the stochastic tamed Navier–Stokes equations (STCNS, for short). Our main goal is to establish the existence and uniqueness of a global strong solution (strong in both the probabilistic and PDE senses) for the 3D STCNS system with large initial data. To achieve this, we first introduce a triple approximation scheme by using the Friedrichs mollifier, frequency truncation operators, and cut-off functions. This scheme enables the construction of sufficiently smooth approximate solutions and facilitates the effective application of the entropy-energy method. Then, based on a newly derived stochastic version of the entropy-energy inequality, we further establish some a priori higher-order energy estimates, which together with the stochastic compactness method, allow us to construct the strong solution for the STCNS system.
The shifted fractional trapezoidal rule (SFTR) with a special shift is adopted to construct a finite difference scheme for the time-fractional Allen-Cahn (tFAC) equation. Some essential key properties of the weights o...
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In this paper, a family of novel energy-preserving schemes are presented for numerically solving highly oscillatory Hamiltonian systems. These schemes are constructed by using the relaxation idea in the extrapolated R...
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In this paper, a consistent and conservative mathematical model is first developed for multiphase electro-hydrodynamic (EHD) flows, which has some distinct features in the volume conservation, the consistency of reduc...
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In this paper, a multiple-distribution-function finite-difference lattice Boltzmann method (MDF-FDLBM) is proposed for the convection-diffusion system based incompressible Navier-Stokes equations (NSEs). By Chapman En...
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