Addendum and Corrigendum to "Local Saturation of Conservative Operators'

In this note we make a correction in the paper [1] by two of the authors. Specifically we modify an auxiliary localization result and prove that the applications to the saturation theory of some outstanding conservative operators remain valid. Moreover, we enrich a corollary dealing with the well-known Szász-Mirakjan operators. This revised version was published online in June 2006 with corrections to the Cover Date.     

GLOBAL EXISTENCE FOR A CLASS OF SYSTEMSOF NONLINEAR WAVE EQUATIONS INTHREE SPACE DIMENSIONS

Consider a system of nonlinear wave equationsfor i = 1, … , m, where F, (i = 1, … , m) are smooth functions of degree 2 near the origin of their arguments, and u = (u1, … ,um), while u and x u represent the first and second derivatives of u, respectively. In this paper, the author presents a new class of nonlineaxity for which the global existence of small solutions is ensured. For example, global existence of small solutions for arbitrary cubic terms,arbitrary cubic termswill be established, provided that c12 ≠ c22.     

Sharp condition of global existence for second-order derivative nonlinear Schrödinger equations in two space dimensions

This paper discusses a class of second-order derivative nonlinear Schrödinger equations which are used to describe the upper-hybrid oscillation propagation. By establishing a variational problem, applying the potential well argument and the concavity method, we prove that there exists a sharp condition for global existence and blow-up of the solutions to the nonlinear Schrödinger equation. In addition, we also answer the question: how small are the initial data, the global solutions exist?     

A Nonlinear Drift - Diffusion System with Electric Convection Arising in Electrophoretic and Semiconductor Modeling

A multi-dimensional transient drift-diffusion model for (at most) three charged particles, consisting of the continuity equations for the concentrations of the species and the Poisson equation for the electric potential, is considered. The diffusion terms depend on the concentrations. Such a system arises in electrophoretic modeling of three species (neutrally, positively and negatively charged) and in semiconductor theory for two species (positively charged holes and negatively charged electrons). Diffusion terms of degenerate type are also possible in semiconductor modeling. For the initial boundary value problem with mixed Dirichlet - Neumann boundary conditions and general reaction rates, a global existence result is proved. Uniqueness of solutions follows in the Dirichlet boundary case if the diffusion terms are uniformly parabolic or if the initial and boundary densities are strictly positive. Finally, we prove that solutions exist which are positive uniformly in time and globally bounded if the reaction rates satisfy appropriate growth conditions.     

具常数存放的非线性功能反应捕食模型的定性分析

研究一类食饵具常数存放且功能反应函数为次线性函数的食饵-捕食者模型,获得了一些平衡点全局渐近稳定,极限环存在惟一的充分条件.利用数值仿真检验了我们的结论.     

Global smooth solutions to the multi-dimensional hydrodynamic model for two-carrier plasmas

The existence of global smooth solutions to the multi-dimensional hydrodynamic model for plasmas of electrons and positively charged ions is shown under the assumption that the initial densities are close to a constant. The model consists of the conservation laws for the particle densities and the current densities, coupled to the Poisson equation for the electrostatic potential. Furthermore, it is proved that the particle densities converge exponentially fast to the (constant) steady state. The proof uses a higher-order energy method inspired from extended thermodynamics.     

Generic existence of Lipschitzian solutions of optimal control problems without convexity assumptions

The Tonelli existence theorem in the calculus of variations and its subsequent modifications were established for integrands f which satisfy convexity and growth conditions. In this paper we consider a large class of optimal control problems which is identified with a complete metric space of integrands without convexity assumptions and show that for a generic integrand the corresponding optimal control problem possesses a unique solution and this solution is Lipschitzian.     

一类退化半导体方程弱解存在性的研究

文章研究了当■(s)=sm(m>1),b(s)=s2和初值为u0,v0∈L 2(Ω)时一类退化半导体方程弱解的存在性．文章首先将原问题正则化,然后对正则化问题在L 2(Ω)空间上做出了有界估计,最后利用收敛性得到了问题的结论．     

Nash平衡的存在性与稳定性

本文对Nash平衡的存在性与稳定性作了较为详细的研究和综述.     

对G.Ladas的一个开问题的解答

本文获得了一个高阶非线性差分方程具有无界正解的充分条件，所得结果解决了G.Ladas提出的一个开问题。