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991.
Optical vortices as topological objects exist ubiquitously in nature. In this paper, we use the principle of variational method and mountain pass lemma to develop some existence theorems for the stationary vortex wave solution of a coupled nonlinear Schrödinger equations, which describe the possibility of effective waveguiding of a weak probe beam via the cross‐phase modulation‐type interaction. The main goal is to obtain a positive solution, of minimal action if possible, with all vector components not identically zero. Additionally, as demanded by beam confinement, we prove the exponential decay of the soliton amplitude at infinity. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
992.
Guangwu Wang Boling Guo Shaomei Fang 《Mathematical Methods in the Applied Sciences》2017,40(14):5262-5272
In this paper, we will firstly extend the results about Jiu, Wang, and Xin (JDE, 2015, 259, 2981–3003). We prove that any smooth solution of compressible fluid will blow up without any restriction about the specific heat ratio γ. Then we prove the blow‐up of smooth solution of compressible Navier–Stokes equations in half space with Navier‐slip boundary. The main ideal is constructing the differential inequality. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
993.
Stability in terms of two measures of solutions to stochastic partial differential delay equations with switching 下载免费PDF全文
In this paper, the problem of stability in terms of two measures is considered for a class of stochastic partial differential delay equations with switching. Sufficient conditions for stability in terms of two measures are obtained based on the technique of constructing a proper approximating strong solution system and conducting a limiting type of argument to pass on stability of strong solutions to mild ones. In particular, the stochastic stability under the fixed‐index sequence monotonicity condition and under the average dwell‐time switching are considered. 相似文献
994.
A second‐order ensemble method based on a blended backward differentiation formula timestepping scheme for time‐dependent Navier–Stokes equations 下载免费PDF全文
Nan Jiang 《Numerical Methods for Partial Differential Equations》2017,33(1):34-61
We present a second‐order ensemble method based on a blended three‐step backward differentiation formula (BDF) timestepping scheme to compute an ensemble of Navier–Stokes equations. Compared with the only existing second‐order ensemble method that combines the two‐step BDF timestepping scheme and a special explicit second‐order Adams–Bashforth treatment of the advection term, this method is more accurate with nominal increase in computational cost. We give comprehensive stability and error analysis for the method. Numerical examples are also provided to verify theoretical results and demonstrate the improved accuracy of the method. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 34–61, 2017 相似文献
995.
In this article, a time discretization decoupled scheme for two‐dimensional magnetohydrodynamics equations is proposed. The almost unconditional stability and convergence of this scheme are provided. The optimal error estimates for velocity and magnet are provided, and the optimal error estimate for pressure are deduced as well. Finite element spatial discretization and numerical implementation are considered in our article (Zhang and He, Comput Math Appl 69 (2015), 1390–1406). © 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 956–973, 2017 相似文献
996.
Modeling social‐ecological systems is difficult due to the complexity of ecosystems and of individual and collective human behavior. Key components of the social‐ecological system are often over‐simplified or omitted. Generalized modeling is a dynamical systems approach that can overcome some of these challenges. It can rigorously analyze qualitative system dynamics such as regime shifts despite incomplete knowledge of the model's constituent processes. Here, we review generalized modeling and use a recent study on the Baltic Sea cod fishery's boom and collapse to demonstrate its application to modeling the dynamics of empirical social‐ecological systems. These empirical applications demand new methods of analysis suited to larger, more complicated generalized models. Generalized modeling is a promising tool for rapidly developing mathematically rigorous, process‐based understanding of a social‐ecological system's dynamics despite limited knowledge of the system. 相似文献
997.
Adrian Falkowski Leszek Słomiński 《Stochastic Processes and their Applications》2017,127(11):3536-3557
We study the existence, uniqueness and stability of solutions of general stochastic differential equations with constraints driven by semimartingales and processes with bounded -variation. Applications to SDEs with constraints driven by fractional Brownian motion and standard Brownian motion are given. 相似文献
998.
结合Plinio等人([Plinio D,Duane G S,Temarn R,Time-dependent attractor for the oscillon equation,Discrete Contin Dyn Syst,2011,29(1):141-167.])提出的时间依赖全局吸引子概念,运用压缩函数的方法,证明了带有时间依赖系数的非自治Plate方程时间依赖拉回吸引子在空间H~4(Ω)∩H~2_0(Ω)×H~2_0(Ω)中的存在性. 相似文献
999.
1000.
We consider a transmission problem consisting of two semilinear parabolic equations involving fractional diffusion operators of different orders in a general non-smooth setting with emphasis on Lipschitz interfaces and transmission conditions along the interface. We give a unified framework for the existence and uniqueness of strong and mild solutions, and their global regularity properties. 相似文献