This paper develops a class of general one-step discretization methods for solving the index-1 stochastic delay differential-algebraic equations. The existence and uniqueness theorem of strong solutions of index-1 equ...
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This paper develops a class of general one-step discretization methods for solving the index-1 stochastic delay differential-algebraic equations. The existence and uniqueness theorem of strong solutions of index-1 equations is given. A strong convergence criterion of the methods is derived, which is applicable to a series of one-step stochastic numerical methods. Some specific numerical methods, such as the Euler-Maruyama method, stochastic ^-methods, split-step ^-methods are proposed, and their strong convergence results are given. Numerical experiments further illustrate the theoretical results.
In this paper we investigate some properties of equilibrium points in n-dimensional linear control systems with saturated state feedback. We provide an index formula for equilibrium points and discuss its relation to ...
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In this paper, we study the following prototypical two-species chemotaxis system with Lotka-Volterra competition and signal production: (Equation presented). We show that if (Equation presented). the associated Neuman...
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In this work, we study global existence, eventual smoothness and asymptotical behavior of positive solutions for the following two-species chemotaxis consumption model: ut = ∆u - χ1∇ · (u∇w), x ∈ Ω, t > 0, ...
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In this paper, we consider the exponential stabilization of coupled wave equations with spatially-varying coefficients and internal anti-damping. In contrast to the previous work in the literature, the kernel equation...
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In this paper, we consider the exponential stabilization of coupled wave equations with spatially-varying coefficients and internal anti-damping. In contrast to the previous work in the literature, the kernel equations of this system are much more complicated. Using the backstepping method, we verify the kernel equations, which is a system of coupled linear wave equations with spatially-varying coefficients. Then by designing a new characteristic line, the well-posedness of the kernel equations is obtained. Finally we use a Lyapunov function to get the exponential stabilization. A numerical example is presented to illustrate the result.
作者：
Zhang, LeiSCHOOL OF MATHEMATICS AND STATISTICS
HUBEI KEY LABORATORY OF ENGINEERING MODELING AND SCIENTIFIC COMPUTING HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY HUBEI WUHAN430074 China
In this paper, we prove global well-posedness of strong solutions to a class of perturbed Camassa-Holm type equations in Besov spaces. It is shown that the existence of global solutions depends only on the L1-integrab...
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In this work, we proposed a diffuse interface model for the dendritic growth with thermosolutal convection. In this model, the sharp boundary between the fluid and solid dendrite is replaced by a thin but nonzero thic...
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In this work, we present the convergence analysis of one-point large deviations rate functions (LDRFs) of the spatial finite difference method (FDM) for stochastic wave equations with small noise, which is essentially...
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In this paper, we propose a sampling algorithm based on state-of-the-art statistical machine learning techniques to obtain conditional nonlinear optimal perturbations (CNOPs), which is different from traditional (dete...
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In this paper, we first present a unified framework of multiple-relaxation-time lattice Boltzmann (MRT-LB) method for the Navier-Stokes and nonlinear convection-diffusion equations where a block-lower-triangular-relax...
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In this paper, we first present a unified framework of multiple-relaxation-time lattice Boltzmann (MRT-LB) method for the Navier-Stokes and nonlinear convection-diffusion equations where a block-lower-triangular-relaxation matrix and an auxiliary source distribution function are introduced. We then conduct a comparison of the four popular analysis methods (Chapman-Enskog analysis, Maxwell iteration, direct Taylor expansion, and recurrence equations approaches) that have been used to obtain the macroscopic Navier-Stokes and nonlinear convection-diffusion equations from the MRT-LB method and show that from mathematical point of view, these four analysis methods can give the same equations at the second-order of expansion parameters. Finally, we give some elements that are needed in the implementation of the MRT-LB method and also find that some available LB models can be obtained from this MRT-LB method.
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