Existence of Solutions to a Singular Initial Value Problem

Under the sign assumptions we investigate the global existence of solutions of the initial value problem x＇ =f（t, x, x＇）, x（0） = A, where the scalar function f（t, x,p） may be singular at x = A.     

General Decay of Solutions of a Nonlinear System of Viscoelastic Equations

In this paper we consider a system of two coupled viscoelastic equations with Dirichlet boundary condition which describes the interaction between two different fields arising in viscoelasticity. For certain class of relaxation functions and certain initial data, we prove that the decay rate of the solution energy is similar to that of relaxation functions which is not necessarily of exponential or polynomial type. This result improves earlier one of Messaoudi and Tatar (Appl. Anal. 87(3):247–263, 2008) and extends some existing results concerning the general decay for a single equation to the case of a system.     

On the Existence of Solutions for a Class of Singular Boundary Value Problem

ＯｎｔｈｅＥｘｉｓｔｅｎｃｅｏｆＳｏｌｕｔｉｏｎｓｆｏｒａＣｌａｓｏｆＳｉｎｇｕｌａｒＢｏｕｎｄａｒｙＶａｌｕｅＰｒｏｂｌｅｍＺｈａｎｇＺｈｉｊｕｎ（张志军）ＸｉａｏＬｉ（萧礼）（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＮｏｒｔｈｗｅｓｔＮｏｒｍａｌＵｎｉｖｅｒ...     

Existence of Solutions of a Two-Point Boundary Value Problem

A two-point boundary value problem with a non-negative parameter Q arising in the study of surface tension induced flow of a liquid metal or semiconductor is studied. We prove that the problem has at least one solution for Q≥0.This improves a recent result that the problem has at least one solution for 0 ≤Q≤13.21.     

Existence and Nonexistence of Global Classical Solutions to Porous Medium and Plasma Equations with Singular Sources

Let Ω be a bounded or unbounded domain in R^n. The initial-boundary value problem for the porous medium and plasma equation with singular terms is considered in this paper. Criteria for the appearance of quenching phenomenon and the existence of global classical solution to the above problem are established. Also, the life span of the quenching solution is estimated or evaluated for some domains.     

The Global Existence of Solutions for a Cross-Diffusion System

ＴｈｅＧｌｏｂａｌＥｘｉｓｔｅｎｃｅｏｆＳｏｌｕｔｉｏｎｓｆｏｒａＣｒｏｓｓ－ＤｉｆｆｕｓｉｏｎＳｙｓｔｅｍ￥（娄元）（倪维明）（吴雅萍）ＹｕａｎＬｏｕ；Ｗｅｉ－ＭｉｎｇＮｉ（ＳｃｈｏｏｌｏｆＭａｔｈｅｍａｔｉｃｓ，ＵｎｉｖｅｒｓｉｔｙｏｆＭｉｎｎｅ...     

The Global Existence of Solutions for a Cross-diffusion System

This paper is concerned with the global existence of solutions for a class of quasilinear cross-diffusion system describing two species competition under self and cross population pressure. By establishing and using more detailed interpolation results between several different Banach spaces, the global existence of solutions are proved when the self and cross diffusion rates for the first species are positive and there is no self or cross-diffusion for the second species.     

Existence of Solutions for Singular Boundary Value Problems

ＥｘｉｓｔｅｎｃｅｏｆＳｏｌｕｔｉｏｎｓｆｏｒＳｉｎｇｕｌａｒＢｏｕｎｄａｒｙＶａｌｕｅＰｒｏｂｌｅｍｓＺｈａｎｇＸｉｋａｎｇ（章熙康）（ＩｎｓｔｉｔｕｔｅｏｆＭａｔｈｅｍａｔｉｃｓ，ＪｉｌｉｎＵｎｉｖｅｒｓｉｔｙ，１３００２３）Ａｂｓｔｒａｃｔ：Ｔ...     

Existence of Nonnegative Solutions to Singular Semi-positone Problems

In this paper we study a class of semi-positone singular boundary value problem. With prior bounds estimate and topology degree method, some existence results of nonnegative solution will be shown.     

Global Existence,Uniqueness and Pathwise Property of Solutions to a Stochastic Rssler-Lorentz System

The authors integrate two well-known systems, the Rssler and Lorentz systems,to introduce a new chaotic system, called the Lorentz-Rssler system. Then, taking into account the effect of environmental noise, the authors incorporate white noise in both Rssler and Lorentz systems to have a corresponding stochastic system. By deriving the uniform a priori estimates for an approximate system and then taking them to the limit,the authors prove the global existence, uniqueness and the pathwise property of solutions to the Lorentz-Rssler system. Moreover, the authors carried out a number of numerical experiments, and the numerical results demonstrate their theoretic analysis and show some new qualitative properties of solutions which reveal that the Lorentz-Ro¨ssler system could be used to design more complex and more secure nonlinear hop-frequence time series.     

Global Existence, Uniqueness and Pathwise Property of Solutions to a Stochastic R¨ossler-Lorentz System

The authors integrate two well-known systems, the R¨ossler and Lorentz systems, to introduce a new chaotic system, called the Lorentz-R¨ossler system. Then, taking into account the effect of environmental noise, the authors incorporate white noise in both R¨ossler and Lorentz systems to have a corresponding stochastic system. By deriving the uniform a priori estimates for an approximate system and then taking them to the limit, the authors prove the global existence, uniqueness and the pathwise property of solutions to the Lorentz-R¨ossler system. Moreover, the authors carried out a number of numerical experiments, and the numerical results demonstrate their theoretic analysis and show some new qualitative properties of solutions which reveal that the Lorentz-R¨ossler system could be used to design more complex and more secure nonlinear hop-frequence time series.     

Existence Theorem of Global Solutions for Monge-Ampere Equation

ＥｘｉｓｔｅｎｃｅＴｈｅｏｒｅｍｏｆＧｌｏｂａｌＳｏｌｕｔｉｏｎｓｆｏｒＭｏｎｇｅ－ＡｍｐｅｒｅＥｑｕａｔｉｏｎｈｏＬｉｊｉａｎｇ（鹿立江）（ＴｉａｎｊｉｎＵｎｉｖｅｒｓｉｔｙｏｆＦｉｎａｎｃｅａｎｄＥｃｏｎｏｍｉｃｓ，Ｔｉａｎｊｉｎ，３００２２２）...     

Existence of Three Solutions for a Degenerate Kirchhoff–Type Transmission Problem

In this article, we establish the existence of three weak solutions for a nonlinear transmission problem involving degenerate nonlocal coefficients of p(x)–Kirchhoff–type. Our approach is of variational nature; the weak formulation takes place in suitable variable exponent Sobolev spaces.     

Numerical Study of Blow up and Stability of Solutions of Generalized Kadomtsev–Petviashvili Equations

We first review the known mathematical results concerning the Kadomtsev–Petviashvili type equations. Then we perform numerical simulations to analyze various qualitative properties of the equations: blow-up versus long time behavior, stability and instability of solitary waves.     

Blow—up of Solutions of Heat Flows for Harmonic Maps

Let (M,g) and (N,h)be two Riemannian manifolds. Consider the heat flow for harmonic maps from (M,g) into (N,h).We prove the following results Suppose dim M =3 and is a nontrivial homotopy class in C(M,N).Then there exists a constant ?o such that if and E(u0)相似文献   

Global Existence of Positive Solutions for Volterra Integral Equations

ＧｌｏｂａｌＥｘｉｓｔｅｎｃｅｏｆＰｏｓｉｔｉｖｅＳｏｌｕｔｉｏｎｓｆｏｒＶｏｌｔｅｒｒａＩｎｔｅｇｒａｌＥｑｕａｔｉｏｎｓＷａｎｇＳｈｕ（王术）；ＷａｎＣｈｕｎｌｉｎ（万春林）；ＺｈａｎｇＫｕｎ（张锟）（ＨｅｍａｎＵｎｉｖｅｒｓｉｔｙ，Ｋａｉｆｅｎ...     

Existence of Positive Solutions to Semipositone Singular Dirichlet Boundary Value Problems

The paper presents the conditions which guarantee that for some positive value of μ there are positive solutions of the differential equation （Ф（x＇））＇＋μQ（t, x, x＇） = 0 satisfying the Dirichlet boundary conditions x（0） = x（T） = 0. Here Q is a continuous function on the set [0, T] × （0, ∞） ~ （R ／ {0}） of the semipositone type and Q is singular at the value zero of its phase variables.