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Search Results: 1 - 10 of 104153 matches for " Zhengce Zhang "
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Liouville-Type Theorems for Some Integral Systems  [PDF]
Zhengce Zhang
Applied Mathematics (AM) , 2010, DOI: 10.4236/am.2010.12012
Abstract: In this paper, Liouville-type theorems of nonnegative solutions for some elliptic integral systems are considered. We use a new type of moving plane method introduced by Chen-Li-Ou. Our new ingredient is the use of Stein-Weiss inequality instead of Maximum Principle.
Solutions with Dead Cores for a Parabolic P-Laplacian Equation  [PDF]
Zhengce Zhang, Yanyan Li
Advances in Pure Mathematics (APM) , 2011, DOI: 10.4236/apm.2011.15050
Abstract: We study the solutions with dead cores and the decay estimates for a parabolic p-Laplacian equation with absorption by sub- and supersolution method. Special attention is given to the case where the solution of the steady-state problem vanishes in an interior region.
Quenching Rate for the Porous Medium Equation with a Singular Boundary Condition  [PDF]
Zhengce Zhang, Yanyan Li
Applied Mathematics (AM) , 2011, DOI: 10.4236/am.2011.29157
Abstract: We study the porous medium equation ut=(um). 0<x<∞, t>0 with a singular boundary condition (um) (0,t)=u(0,t). We prove finite time quenching for the solution at the boundary χ=0. We also establish the quenching rate and asymptotic behavior on the quenching point.
Boundedness of Global Solutions for a Heat Equation with Exponential Gradient Source
Zhengce Zhang,Yanyan Li
Abstract and Applied Analysis , 2012, DOI: 10.1155/2012/398049
Abstract: We consider a one-dimensional semilinear parabolic equation with exponential gradient source and provide a complete classification of large time behavior of the classical solutions: either the space derivative of the solution blows up in finite time with the solution itself remaining bounded or the solution is global and converges in 1 norm to the unique steady state. The main difficulty is to prove 1 boundedness of all global solutions. To do so, we explicitly compute a nontrivial Lyapunov's functional by carrying out the method of Zelenyak.
Nonexistence and Radial Symmetry of Positive Solutions of Semilinear Elliptic Systems
Zhengce Zhang,Liping Zhu
Discrete Dynamics in Nature and Society , 2009, DOI: 10.1155/2009/629749
Abstract: Nonexistence and radial symmetry of positive solutions for a class of semilinear elliptic systems are considered via the method of moving spheres.
Spatial Profile of the Dead Core for the Fast Diffusion Equation with Dependent Coefficient
Zhengce Zhang,Biao Wang
International Journal of Differential Equations , 2011, DOI: 10.1155/2011/751969
Abstract: We consider the dead-core problem for the fast diffusion equation with spatially dependent coefficient and obtain precise estimates on the single-point final dead-core profile. The proofs rely on maximum principle and require much delicate computation. 1. Introduction In this paper, we study the porous medium equation with the following initial boundary condition: where and . Assume and that the initial data satisfies Moreover, we denote Here we are mainly interested in the asymptotic behavior of nonnegative and global classical solutions. However, Problem (1.1) is singular at for . In fact, the solutions can be approximated, if necessary, by the ones satisfying the following equation with the same initial-boundary value conditions and taking the limit . We set and denote For suitable initial data, we will show that (see Theorem 1.1). We say that the solution develops a dead core in finite time, and is called the dead-core time. In the past few years, much attentions have been taken to the dead-core problems. For the semilinear case of and , the temporal dead-core profile was investigated in [1] by Guo and Souplet. For the quasilinear case of and , Guo et al. [2] firstly investigated the solution which develops a dead core in finite time; then they obtained the spatial profile of the dead core and also studied the non-self-similar dead-core rate of the solution. Numerous related works have been devoted to some of the regularity and the corresponding problems such as blowup, quenching, and gradient blowup; we refer the interested reader to [3–11] and the references therein. Our aim of this paper is to study the dead-core problem for the fast diffusion with strong absorption. In view of the observation concerning the interaction of diffusion and absorption, this question is of interest since the effect of fast diffusion, as compared with linear diffusion, is much stronger near the level . Although our strategy of proof is close to that in [2], the proof is technically much more difficult due to the presence of a nonlinear operator and spatially dependent absorption coefficient. The paper is organized as follows. In Section 2, we prove that the solution of the porous medium equation develops a dead core in finite time. In Section 3, firstly, we obtain the spatial profile of the dead-core upper bound estimate by the initial monotone assumption; then we construct auxiliary function and derive the lower bound estimate by maximum principle. Our first result gives sufficient conditions under which the solution of Problem (1.1) develops a dead core in finite
An Efficient and Concise Algorithm for Convex Quadratic Programming and Its Application to Markowitz’s Portfolio Selection Model  [PDF]
Zhongzhen Zhang, Huayu Zhang
Technology and Investment (TI) , 2011, DOI: 10.4236/ti.2011.24024
Abstract: This paper presents a pivoting-based method for solving convex quadratic programming and then shows how to use it together with a parameter technique to solve mean-variance portfolio selection problems.
Investigation and Analysis of Sexual Harassment in Corporate Workplace of China  [PDF]
Xiaobing Zhang, Zewei Zhang
Sociology Mind (SM) , 2012, DOI: 10.4236/sm.2012.23038
Abstract: At present, sexual harassment in domestic workplace has a high probability of occurrence, which causes more and more attention. In this paper, the form of sexual harassment in workplace, and how to solve the sexual harassment were investigated and analyzed through questionnaires; and countermeasures and management suggestions were put forward from three aspects of corporate, employees and family.
Chaos Control in a Discrete Ecological System  [PDF]
Limin Zhang, Chaofeng Zhang
International Journal of Modern Nonlinear Theory and Application (IJMNTA) , 2012, DOI: 10.4236/ijmnta.2012.13011
Abstract: In research [1], the authors investigate the dynamic behaviors of a discrete ecological system. The period-double bifurcations and chaos are found in the system. But no strategy is proposed to control the chaos. It is well known that chaos control is the first step of utilizing chaos. In this paper, a controller is designed to stabilize the chaotic orbits and enable them to be an ideal target one. After that, numerical simulations are presented to show the correctness of theoretical analysis.
Crystallization and Characterization of a New Fluorescent Molecule Based on Schiff Base  [PDF]
Dehua Zhang, Xiaoyan Zhang
Journal of Crystallization Process and Technology (JCPT) , 2013, DOI: 10.4236/jcpt.2013.31004

In this analysis, the single crystal of schiff base has been synthesized and the purity of material has been increased by repeated recrystallization process. Single crystal was grown by adopting the method growing in a slow evaporation solution using ethanol as solvent at room temperature. A new fluorescent molecule based on Schiff base has been synthesised and its binding properties investigated by fluorescence spectroscopy to show that it can selectively bind Cu2+ with fluorescence quenching.

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