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Communications in Theoretical Physics

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Communications in Theoretical Physics 2020年第5期72卷 1-12页

作者： Zhi-zhong tan Zhen tan Department of Physics Nantong UniversityNantong226019China School of Information Science and Technology Nantong UniversityNantong 226019China

The unified processing and research of multiple network models are implemented,and a new theoretical advance has been made,which sets up two new theorems on evaluating the exact electrical characteristics(potential and resistance)of the complex m×n resistor networks by the recursion-transform method with potential parameters,and applies to a variety of different types of lattice structure with arbitrary boundaries such as the nonregular m×n rectangular networks and the nonregular m×n cylindrical *** research gives the analytical solutions of electrical characteristics of the complex networks(finite,semi-infinite and infinite),which has not been solved *** applications of the theorems,a series of analytical solutions of potential and resistance of the complex resistor networks are discovered.

关键词： complex network RT-V method electrical properties boundary conditions Laplace equation mathematical physics

Electrical properties of m×n cylindrical network

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Chinese Physics B 2020年第8期29卷 182-197页

作者： Zhi-zhong tan Zhen tan Department of Physics Nantong UniversityNantong 226019China School of Information Science and Technology Nantong UniversityNantong 226019China

We consider the problem of electrical properties of an m×n cylindrical network with two arbitrary boundaries,which contains multiple topological network models such as the regular cylindrical network,cobweb network,globe network,and so *** deduce three new and concise analytical formulae of potential and equivalent resistance for the complex network of cylinders by using the RT-V method(a recursion-transform method based on node potentials).To illustrate the multiplicity of the results we give a series of special ***,the results obtained from the resistance formulas of cobweb network and globe network obtained are different from the results of previous studies,which indicates that our research work creates new research ideas and *** a byproduct of the study,a new mathematical identity is discovered in the comparative study.

关键词： cylindrical network complex boundaries RT-V method electrical properties Laplace equation

The Limit Theorems for Maxima of Stationary Gaussian Processes with Random Index

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Acta Mathematica Sinica,English Series 2014年第6期30卷 1021-1032页

作者： zhong Quan tan College of Mathematics Physics and Information Engineering Jiaxing University

Let {X（t）, t ≥ 0} be a standard（zero-mean, unit-variance） stationary Gaussian process with correlation function r（·） and continuous sample paths. In this paper, we consider the maxima M（T） = max{X（t）, t∈ [0, T ]} with random index TT, where TT /T converges to a non-degenerate distribution or to a positive random variable in probability, and show that the limit distribution of M（TT） exists under some additional conditions related to the correlation function r（·）.

关键词： Limit theorem weak convergence maximum random index stationary Gaussian process

Global Existence of Strong Solutions of Navier-Stokes-Poisson Equations for One-Dimensional Isentropic Compressible Fluids

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Chinese Annals of Mathematics,Series B 2008年第4期29卷 441-458页

作者： Junping YIN zhong tan Department of Mathematics Xiamen University Xiamen 361005 Fujian China.

The authors prove two global existence results of strong solutions of the isentropic compressible Navier-Stokes-Poisson equations in one-dimensional bounded intervals. The first result shows only the existence. And the second one shows the existence and uniqueness result based on the first result, but the uniqueness requires some compatibility condition. In this paper the initial vacuum is allowed, and T is bounded.

关键词： Global strong solutions Navier-Stokes-Poisson equations Existence and uniqueness

Existence of Three Solutions for Quasilinear Elliptic Equations: an Orlicz-Sobolev Space Setting

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Acta Mathematicae Applicatae Sinica 2017年第2期33卷 287-296页

作者： Fei FANG zhong tan Department of Mathematics Beijing Technology and Business University School of Mathematical Sciences Xiamen University

In this paper, we establish the existence of three weak solutions for quasilinear elliptic equations in an Orlicz-Sobolev space via an abstract result recently obtained by Ricceri in [13].

关键词： Orlicz-Sobolev spaces quasilinear elliptic equations three critical points theorem

Behavior of solutions to a Petrovsky equation with damping and variable-exponent sources

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Science China Mathematics 2023年第2期66卷 285-302页

作者： Menglan Liao zhong tan School of Mathematical Sciences Xiamen UniversityXiamen 361005China

This paper deals with the following Petrovsky equation with damping and nonlinear sources:utt+△^(2)u-M(||■u||2^(2))△ut+|ut|^(m(x)-2)ut=|u|^(p(x)-2)u under initial-boundary value conditions,where M(s)=a+b sγis a positive C 1 function with the parameters a>0,b>0,γ≥1,and m(x)and p(x)are given measurable *** upper bound of the blow-up time is derived for low initial energy by the differential inequality *** m(x)≡2,in particular,the upper bound of the blow-up time is obtained by the combination of Levine's concavity method and some differential inequalities under high initial *** addition,we discuss the lower bound of the blow-up time by making full use of the strong ***,we present the global existence of solutions and an energy decay estimate by establishing some energy estimates.

关键词： Petrovsky equation damping variable-exponent source blow-up energy decay rate

Propagation of Density-Oscillations in Solutions to the Compressible Navier-Stokes-Poisson System

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Chinese Annals of Mathematics,Series B 2008年第5期29卷 501-520页

作者： zhong tan Yanjin WANG Department of Mathematics Xiamen University Xiamen 361005 Fujian China Department of Mathematics Xiamen UniversityXiamen 3610051 Fujian China

Concerning a bounded sequence of finite energy weak solutions to the compressible Navier-Stokes-Poisson system (denoted by CNSP), which converges up to extraction of a subsequence, the limit system may not be the same system. By introducing Young measures as in [6, 15], the authors deduce the system (HCNSP) which the limit functions must satisfy. Then they solve this system in a subclass where Young measures are convex combinations of Dirac measures, to give the information on the propagation of density-oscillations. The results for strong solutions to (CNSP) (see Corollary 6.1) are also obtained.

关键词： Compressible fluids Navier-Stokes-Poisson equations Young measures Propagation of oscillations Strong solutions

Blow-up of Viscous Compressible Reactive Self-gravitating Gas

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Acta Mathematicae Applicatae Sinica 2012年第2期28卷 401-408页

作者： Fei JIANG zhong tan School of Mathematical Sciences Xiamen University Xiamen 361005 China Institute of Applied Physics and Computational Mathematics l~eijlng IUUUI~ L）hma

In this paper, we prove some results concerning blow-up of viscous compressible reactive （selfgravitating） flows when the initial density is compactly supported and the other initial value satisfy proper conditions. It extends the work of Xin and Cho to the case of viscous compressible reactive self-gravitating flows equations. We control the lower bound of second moment by total energy and obtain the precise relationship between the size of the support of initial density and the existence time.

关键词： compressible Naviver-Stokes equations smooth solution reactive self-gravitating gas

Asymptotic stability of explicit infinite energy blowup solutions of the 3D incompressible Navier-Stokes equations

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Science China Mathematics 2023年第11期66卷 2523-2544页

作者： Fangyu Han zhong tan School of Mathematical Sciences Xiamen UniversityXiamen 361005China Fujian Provincial Key Laboratory on Mathematical Modeling and High-Performance Scientific Computing Xiamen UniversityXiamen UniversityXiamen 361005China Shenzhen Research Institute of Xiamen University Shenzhen 518057China

In this paper,we study the dynamical stability of a family of explicit blowup solutions of the threedimensional(3D)incompressible Navier-Stokes(NS)equations with smooth initial values,which is constructed in Guo et al.(2008).This family of solutions has finite energy in any bounded domain of R3,but unbounded energy in *** on similarity coordinates,energy estimates and the Nash-Moser-H?rmander iteration scheme,we show that these solutions are asymptotically stable in the backward light-cone of the ***,the result shows the existence of local energy blowup solutions to the 3D incompressible NS equations with growing ***,the result also shows that in the absence of physical boundaries,the viscous vanishing limit of the solutions does not satisfy the 3D incompressible Euler equations.

关键词： Navier-Stokes equations asymptotic stability blowup solution infinite energy Nash-Moser-Hormander iteration scheme zero-viscosity limit