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Free Boundary Problems with Local-nonlocal Diffusions and Different Free Boundaries Ⅰ: Global Solution

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Acta Mathematica Sinica,English Series 2022年第12期38卷 2265-2284页

作者： Xiu DONG Jian Ping wang ming xin wang School of Mathematics Harbin Institute of TechnologyHarbin 150001P.R.China School of Applied Mathematics Xiamen University of TechnologyXiamen 361024P.R.China School of Mathematics and Information Science Henan Polytechnic UniversityJiaozuo 454000P.R.China

We investigate a class of ecological models with local-nonlocal diffusions and different free *** is PartⅠof a two-part series,in which the existence,uniqueness,regularity and estimates of global solution is *** spreading-vanishing dichotomy,criteria governing spreading and vanishing,long-time behavior of solution and the estimation of the spreading speed when spreading happens will be studied in the separate PartⅡ.

关键词： Local-nonlocal diffusions different free boundaries existence-uniqueness global solution

Structure of Coexistence States for a Class of Quasilinear Elliptic Systems

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Acta Mathematica Sinica,English Series 2007年第9期23卷 1649-1662页

作者： Guo Ying YANG ming xin wang Department of Mathematics He'nan Polytechnic University Jiaozuo 454003 P. R. China Department of Mathematics Xuzhou Normal University Xuzhou 221116 P. R. China and Department of Mathematics Southeast University Nanjing 210018 P. R. China

The structure of positive solutions of the p-Laplacian systems is discussed via bifurcation theory and monotone techniques.

关键词： coexistence states quasilinear elliptic systems bifurcation

On pattern formation in the Gray-Scott model

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Science China Mathematics 2007年第3期50卷 377-386页

作者： Rui PENG ming-xin wang Institute of Nonlinear Complex Systems China Three Gorges UniversityYichang 443002China Department of Mathematics Southeast UniversityNanjing 210018China

In the paper, we investigate an elliptic system well-known as the Gray-Scott model and present some further results for positive solutions of this model. More precisely, we give the refined a priori estimates of positive solutions, and improve some previous results for the non-existence and existence of positive non-constant solutions as the parameters are varied, which imply some certain conditions where the pattern formation occurs or not.

关键词： Gray-Scott model pattern formation a priori estimates existence 35J55 92C15 92C40

Properties of positive solutions to a nonlinear parabolic problem

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Science China Mathematics 2007年第4期50卷 590-608页

作者： Hui-ling LI ming-xin wang Department of Mathematics Southeast UniversityNanjing 210018China

This paper deals with the properties of positive solutions to a quasilinear parabolic equation with the nonlinear absorption and the boundary flux. The necessary and sufficient conditions on the global existence of solutions are described in terms of different parameters appearing in this problem. Moreover, by a result of Chasseign and Vázquez and the comparison principle, we deduce that the blow-up occurs only on the boundary ?Ω. In addition, for a bounded Lipschitz domain Ω, we establish the blow-up rate estimates for the positive solution to this problem with a = 0.

关键词： quasilinear parabolic equation blow-up global existence blow-up rate blow-up set 35K60 35B40 35K65

A Note on a Diffusive Predator-prey Model and Its Steady-state System

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Acta Mathematica Sinica,English Series 2010年第5期26卷 963-974页

作者： Rui PENG ming xin wang Guo Ying YANG Institute of Nonlinear Complex Systems College of Science China Three Gorges University Yichang 443002 P. R. China Department of Mathematics Southeast University Nanjing 210096 P. R. China Department of Mathematics Henan Polytechnic University Jiaozuo 454100 P. R. China

In this note, a diffusive predator-prey model subject to the homogeneous Neumann bound- ary condition is investigated and some qualitative analysis of solutions to this reaction-diffusion system and its corresponding steady-state problem is presented. In particular, by use of a Lyapunov function, the global stability of the constant positive steady state is discussed. For the associated steady state problem, a priori estimates for positive steady states are derived and some non-existence results for non-constant positive steady states are also established when one of the diffusion rates is large enough. Consequently, our results extend and complement the existing ones on this model.

关键词： a diffusive predator-prey model steady states global stability a priori-estimates non-existence

Positive Steady States of a Prey-predator Model with Diffusion and Non-monotone Conversion Rate

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Acta Mathematica Sinica,English Series 2007年第4期23卷 749-760页

作者： Rui PENG ming xin wang Wen Van CHEN Institute of Nonlinear Complex System College of Science China Three Gorges University Yichang 443002 P. R. China Department of Mathematics Southeast University Nanjing 210018 P. R. China Department of Mathematics Xuzhou Normal University Xuzhou 221116 P. R. China

In this paper, we study the positive steady states of a prey-predator model with diffusion throughout and a non-monotone conversion rate under the homogeneous Dirichlet boundary condition. We obtain some results of the existence and non-existence of positive steady states. The stability and uniqueness of positive steady states are also discussed.

关键词： prey-predator model Steady states Existence Uniqueness Stability

Qualitative Analysis of a Belousov–Zhabotinskii Reaction Model

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Acta Mathematica Sinica,English Series 2018年第6期34卷 975-991页

作者： Aung Zaw MYINT Li LI ming xin wang Department of Mathematics Harbin Institute of Technology

This paper deals with one kind of Belousov-Zhabotinskii reaction model. Linear stability is discussed for the spatially homogeneous problem firstly. Then we focus on the stationary problem with diffusion. Non-existence and existence of non-constant positive solutions are obtained by using implicit function theorem and Leray-Sehauder degree theory, respectively.

关键词： Belousov-Zhabotinskii reaction stability positive stationary solutions

Noble metal-based high-entropy alloys as advanced electrocatalysts for energy conversion

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Rare Metals 2021年第9期40卷 2354-2368页

作者： Yu-Chen Qin Feng-Qi wang xin-ming wang ming-Wei wang Wen-Long Zhang Wan-Kai An Xiao-Peng wang Yun-Lai Ren xin Zheng Dong-Can Lv Ayyaz Ahmad College of Sciences Henan Agricultural UniversityZhengzhou 450000China State-Key Laboratory of Chemical Engineering and Shanghai Key Laboratory of Multiphase Materials Chemical EngineeringEast China University of Science and TechnologyShanghai 200237China Department of chemical Engineering MNS University of Engineering and Technology Multan 60000Pakistan

Noble metal-based high-entropy alloy nanoparticles(NM-HEA NPs) have exhibited brilliant catalytic performance toward electrocatalytic energy conversion and attracted increasing attention. The near-equimolar mixed elements of NM-HEA NPs may result in the unique properties including cocktail effect, high entropy effect and lattice distortion effect, which are beneficial for improving the catalytic performance and reducing the amount of noble metal. Herein, several advanced NM-HEA NPs as electrocatalysts for energy conversion are systematically summarized. The preparation methods of NM-HEA NPs are evaluated as well as the catalytic properties and mechanism are discussed classified by electrocatalytic reactions. Finally,the challenges and prospects in this field are carefully discussed. This review provides an overview on recent advances of NM-HEA electrocatalysts for energy conversion and draws more attention in this infant research field.

关键词： Noble metal-based high-entropy alloys Electrocatalysis Energy conversion Synthesis Catalytic performance

The Effect of Potassium Citrate on Simultaneous Growth of Calcium Oxalate Mono-, Di-, and Trihydrate in Synthetic Urine

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Chinese Chemical Letters 2006年第5期17卷 687-690页

作者： Yi ming LIU Feng xin wang Sui Ping DENG Jian ming OUYANG Institute of Biomineralization and Lithiasis Research Jinan University Guangzhou 510632

The inducing effect of potassium citrate （K3cit） on simultaneous growth of calcium oxalate mono-（COM）, di-（COD）, and trihydrate （COT） crystals in synthetic urine was observed with double diffusion gelatinous technique. K3cit can induce the formation of COD and COT, inhibit the aggregation and decrease the surface area of COM crystals. It supported the clinical use of K3cit and may provide important clues to this disease in cure and in search for new drugs.

关键词： Calcium oxalate potassium citrate biomineralization urinary stone gel.