Existence of Monotone Positive Solution for a Fourth-Order Three-Point BVP with Sign-Changing Green’s Function

This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.

GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR FOR THE 3D COMPRESSIBLE NON–ISENTROPIC EULER EQUATIONS WITH DAMPING

We investigate the global existence and asymptotic behavior of classical solutions for the 3D compressible non-isentropic damped Euler equations on a periodic domain. The global existence and uniqueness of classical solutions are obtained when the initial data is near an equilibrium. Furthermore, the exponential convergence rates of the pressure and velocity are also proved by delicate energy methods.

EXISTENCE AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO A SINGULAR PARABOLIC EQUATION

In this paper,we study the initial-boundary value problem for a class of singular parabolic equations.Under some conditions,we obtain the existence and asymptotic behavior of solutions to the problem by parabolic regularization method and the sub-super solutions method.As a byproduct,we prove the existence of solutions to some problems with gradient terms,which blow up on the boundary.

Global Existence and Large Time Asymptotic Behavior of Strong Solution to the Cauchy Problem of 2D Density-Dependent Boussinesq Equations with Vacuum

We dedicate to the 2D density-dependent nonhomogeneous incompressible Boussinesq equations with vacuum on . At infinity, if the attenuation of initial density and temperature is not very slow. And it is gained that there is a global strong solution and is unique for the 2D Cauchy problem with the initial density which can allow vacuum conditions and even have compact support. Besides, the large time decay rates of the gradients of velocity, temperature and pressure can also be obtained which are also the same as those of the homogeneous case.

GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR SOME COUPLED SYSTEMS VIA A LYAPUNOV FUNCTIONAL

The purpose of this work is to study the global existence and asymptotic behavior of solutions to a coupled reaction-diffusion system describing epidemiological or chemical situations. Our analytical proofs are based on the Lyapunov functional methods.

GLOBAL EXISTENCE AND LARGE TIME BEHAVIOR OF SOLUTION TO REACTING FLOW MODEL WITH BOUNDARY EFFECT

The initial boundary value problem (IBVP) for the 3×3 hyperbolic system of reacting flow with source term proposed by R.J.LeVeque and others (see [8]) is considered.It is shown, in the present paper, that if the initial data are a suitable perturbation of a shiftcd shock profile which is suitably away from the boundary, then there exists a unique smooth solution in R2+ to the IBVP of the 3×3 hyperbolic system, which tends to another shifted shock profile of this system as t →∞.

THE EXISTENCE AND GLOBAL OPTIMAL ASYMPTOTIC BEHAVIOUR OF LARGE SOLUTIONS FOR A SEMILINEAR ELLIPTIC PROBLEM

By Karamata regular variation theory and constructing comparison functions, the author shows the existence and global optimal asymptotic behaviour of solutions for a semilinear elliptic problem Δu = k（x）g（u）, u 〉 0, x ∈ Ω, u｜δΩ =＋∞, where Ω is a bounded domain with smooth boundary in R^N; g ∈ C^1[0, ∞）, g（0） = g＇（0） = 0, and there exists p 〉 1, such that lim g（sξ）/g（s）=ξ^p, ↓Aξ 〉 0, and k ∈ Cloc^α（Ω） is non-negative non-trivial in D which may be singular on the boundary.

Global Existence, Asympotic Behavior and Uniform Attractors for Thermoelastic Systems

In this paper, we first establish the global existence and asymptotic behavior of solutions by multiplicative techniques, then further prove the existence of a uniform attractor for a thermoelastic system by using the method of uniform contractive functions. We finally investigate an alternative result of solutions for the semilinear thermoelastic systems by virtue of the semigroup method.

Global Existence,Asymptotic Behavior and Uniform Attractors of Timoshenko Systems with Gurtin-Pipkin Thermal Law

In this paper,we first establish the global existence and asymptotic behavior of solutions by using the semigroup method and multiplicative techniques,then further prove the existence of a uniform attractor for Timoshenko systems with Gurtin-Pipkin thermal law by using the method of uniform contractive functions.The main advantages of this method is that we need only to verify compactness condition with the same type of energy estimates as that for establishing absorbing sets.Moreover,we also investigate an alternative result of solutions to the semilinear Timoshenko systems by virtue of the semigroup method.

Global Existence, Asymptotic Behavior and Uniform Attractors for Damped Timoshenko Systems

In this paper, we consider the Timoshenko system as an initial-boundary value problem in a one-dimensional bounded domain. And then we establish the global existence and asymptotic behavior of solution by using the semigroup method and multiplicative techniques, then further prove the existence of a uniform attractor by using the method of uniform contractive function. The main advantage of this method is that we need only to verify compactness condition with the same type of energy estimate as that for establishing absorbing sets.

Global Existence and Asymptotic Behavior of Non-autonomous Timoshenko Systems

Considering Timoshenko systems under the Cattaneo thermal law, the purpose of the article is to obtain the global existence of linear Timoshenko system and semilinear Timoshenko system for the solutions of non-autonomous situations. The main method is converting the systems into abstract ODE, constructing proper spaces and proving the global existence by using semigroup methods. For asymptotic behavior, there will be a remark to describe the results.

THE EXISTENCE AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR EVOLUTION EQUATIONS AND APPLICATIONS TO P. D. E.

The main purpose of this paper is to discuss the existence and asymptotic behavior of solutions for [GRAPHICS] and for which the sufficient conditions of asymptotic behavior are obtained and the restriction for the existence is reduced.

Global Existence of the Solution for a Reduced Model of the Vectorial Quantum Zakharov System

In this paper, we study the global existence of the smooth solution for a reduced quantum Zakharov system in two spatial dimensions. Using energy estimates and the logarithmic type Sobolev inequality, we show the global existence of the solution to this system without any small condition on the initial data.

ASYMPTOTIC BEHAVIOR OF SOLUTION FOR NONLOCAL REACTION-DIFFUSION SYSTEM

This paper deals with reaction-diffusion system with nonlocal source. It is proved that there exists a unique classical solution and the solution either exists globally or blows up in finite time. Furthermore, its blow-up set and asymptotic behavior are obtained provided that the solution blows up in finite time.

Existence and iteration of monotone positive solutions for a third-order two-point boundary value problem

The existence of nondecreasing positive solutions for the nonlinear third-order twopoint boundary value problem u′″（t） ＋ q（t）f（t,u（t）,u′（t）） = 0, 0 〈 t 〈 1, u（0） = u″（0） = u′（1） = 0 is studied. The iterative schemes for approximating the solutions are obtained by applying a monotone iterative method.

LARGE-TIME BEHAVIOR OF SOLUTIONS OF QUANTUM HYDRODYNAMIC MODEL FOR SEMICONDUCTORS

A one-dimensional quantum hydrodynamic model （or quantum Euler-Poisson system） for semiconductors with initial boundary conditions is considered for general pressure-density function. The existence and uniqueness of the classical solution of the corresponding steady-state quantum hydrodynamic equations is proved. Furthermore, the global existence of classical solution, when the initial datum is a perturbation of t he steadystate solution, is obtained. This solution tends to the corresponding steady-state solution exponentially fast as the time tends to infinity.

LARGE TIME BEHAVIOR OF GLOBAL STRONG SOLUTIONS TO A TWO-PHASE MODEL WITH A MAGNETIC FIELD

In this paper,the Cauchy problem for a two-phase model with a magnetic field in three dimensions is considered.Based on a new linearized system with respect to(c−c_(∞),P−P_(∞),u,H)for constants c_(∞)≥0 and P_(∞)>0,the existence theory of global strong solution is established when the initial data is close to its equilibrium in three dimensions for the small H^(2) initial data.We improve the existence results obtained by Wen and Zhu in[40]where an additional assumption that the initial perturbations are bounded in L^(1)-norm was needed.The energy method combined with the low-frequency and high-frequency decomposition is used to derive the decay of the solution and hence the global existence.As a by-product,the time decay estimates of the solution and its derivatives in the L^(2)-norm are obtained.

Global Existence in H^2 for a 1-d Non-monotone Fluid

In this paper, we prove the existence in H＋^2, an incomplete metric subspace of H^2×H^2×H^2, of global solutions to the system for a one-dimensional non-monotone fluid in bounded domainΩ=（0,1）. The results in this paper have improved those previously related results.

A Remark on Global Existence in H^4 for a Nonlinear Thermoviscoelasticity Equations with Non-monotone Pressure

We consider a one-dimensional continuous model of nutron star, described by a compressible thermoviscoelastic system with a non-monotone equation of state, due to the effective Skyrme nuclear interaction between particles. We will prove that, despite a possible destabilizing influence of the pressure, which is non-monotone and not always positive, the presence of viscosity and a sufficient thermal dissipation describe the global existence of solutions in H^4 with a mixed free boundary problem for our model.

Approximate Solutions to the Discontinuous Riemann-Hilbert Problem of Elliptic Systems of First Order Complex Equations

Several approximate methods have been used to find approximate solutions of elliptic systems of first order equations. One common method is the Newton imbedding approach, i.e. the parameter extension method. In this article, we discuss approximate solutions to discontinuous Riemann-Hilbert boundary value problems, which have various applications in mechanics and physics. We first formulate the discontinuous Riemann-Hilbert problem for elliptic systems of first order complex equations in multiply connected domains and its modified well-posedness, then use the parameter extensional method to find approximate solutions to the modified boundary value problem for elliptic complex systems of first order equations, and then provide the error estimate of approximate solutions for the discontinuous boundary value problem.