Asymptotic analysis of Emden–Fowler type equation with an application to power flow models

Emden–Fowler type equations are nonlinear differential equations that appear in many fields such as mathematical physics, astrophysics and chemistry. In this paper, we perform an asymptotic analysis of a specific Emden–Fowler type equation that emerges in a queuing theory context as an approximation of voltages under a well-known power flow model. Thus, we place Emden–Fowler type equations in the context of electrical engineering. We derive properties of the continuous solution of this specific Emden–Fowler type equation and study the asymptotic behavior of its discrete analog. We conclude that the discrete analog has the same asymptotic behavior as the classical continuous Emden–Fowler type equation that we consider.     

Gap functions and global error bounds for differential variational–hemivariational inequalities

This paper concerns with the study of a differential variational–hemivariational inequality (DVHVI, for short) in infinite-dimensional Banach spaces. We first introduce the new concept of gap functions for the variational control system of (DVHVI). Then, we consider two kinds of gap functions which are regularized gap function and Moreau–Yosida regularized gap function, respectively, and examine the relevant properties of the gap functions. Moreover, two global error bounds which depend implicitly on the regularized gap function and the Moreau–Yosida regularized gap function, accordingly, are obtained. Finally, in order to illustrate the applicability of the theoretical results, we investigate a coupled dynamic system which is formulated by a nonlinear reaction–diffusion equation described by a time-dependent nonsmooth semipermeability problem.     

A Unified and Explicit Construction of N-Soliton Solutions for the Nonlinear Schrödinger Equation

An explicit N-fold Darboux transformation with multiparameters for nonlinear Schrödinger equation is constructed with the help of its Lax pairs and a reduction technique. According to this Darboux transformation, the solutions of the nonlinear Schrödinger equation are reduced to solving a linear algebraic system, from which a unified and explicit formulation of N-soliton solutions with multiparameters for the nonlinear Schrödinger equation is given.     

半透明介质中辐射传递方程的反演计算及数值模拟

本文介绍了一侧为半透明、另一侧为非透明界面时一维半透明介质的辐射强度计算式。采用辐射与导热复合换热模型计算半透明介质内温度场。利用已知的温度场求半透明介质的辐射强度一正问题计算。将此辐射强度代入辐射反问题计算模型，引入测量误差，采用Ｃｈａｈｉｎｅ方法及演半透明介质内温度场一反问题计算。数值模拟表明，本文所采用的辐射反演法具有较高的精度及稳定性。     

Global existence inL 1 for the modified nonlinear Enskog equation in ℝ3

A global existence theorem with large initial data inL ¹ is given for the modified Enskog equation in ³. The method, which is based on the existence of a Liapunov functional (analog of theH-Boltzmann theorem), utilizes a weak compactness argument inL ¹ in a similar way to the DiPerna-Lions proof for the Boltzmann equation. The existence theorem is obtained under certain condition on the behavior of the geometric factorY. The condition onY amounts to the fact that theL ¹ norm of the collision term grows linearly when the local density tends to infinity.     

Phase space density representations in fluid dynamics

Phase space density representations of inviscid fluid dynamics were recently discussed by Abarbanel and Rouhi. Here it is shown that such representations may be simply derived and interpreted by means of the Liouville equation corresponding to the dynamical system of ordinary differential equations that describes fluid particle trajectories. The Hamiltonian and Poisson bracket for the phase space density then emerge as immediate consequences of the corresponding structure of the dynamics. For barotropic fluids, this approach leads by direct construction to the formulation presented by Abarbanel and Rouhi. Extensions of this formulation to inhomogeneous incompressible fluids and to fluids in which the state equation involves an additional transported scalar variable are constructed by augmenting the single-particle dynamics and phase space to include the relevant additional variable.