THE EXISTENCE, UNIQUENESS AND STABILITY OF ALMOST PERIODIC SOLUTION FOR A CLASS OF NONLINEAR SYSTEM

In this paper, we study the problems on the existence, uniqueness and stability of almost periodic solution for a class of nonlinear system. Using fixed point theorem and Lyapunov functional, the sufficient conditions are given which guarantee the existence, uniqueness and stability of almost periodic solution for the system.     

EXISTENCE AND UNIQUENESS OF THE SOLUTION FOR A CLASS OF NONLINEAR FRACTIONAL DIFFERENTIAL SYSTEM

In this paper we prove the existence and uniqueness of the solution for a class of nonlinear fractional differential system, and investigate the dependence of the solution on the orderαi.     

GENERIC STABILITY AND EXISTENCE OF ESSENTIAL COMPONENTS OF THE SOLUTION SET FOR THE SYSTEM OF GENERALIZED VECTOR EQUILIBRIUM PROBLEMS

By using Fort theorem the generic stability result for the system of generalized vector equilibrium problems is established.Further,by proving the existence and connectivity of minimal essential set the existence result of essential components in the solution set is derived.     

THE EXISTENCE OF THE SOLUTIONS FOR A CLASS OF SEMILINEAR EVOLUTION EQUATIONS

The author obtains the existence of the local and global solution for a class of semilinear evolution equations in a Hilbert spcae, and uses the results to prove the existence of the solution for semilinear parabolic partial differential equations in R~n.     

EXISTENCE OF COUPLED WEAK QUASISOLUTIONS OF SYSTEMS OF QUASILINEAR ELLIPTIC BOUNDARY VALUE PROBLEMS

In this paper, we use the upper-lower solution method with the theory of monotone operators to obtain the existence of coupled weak quasi-solutions of the following boundary value problem for quasilinear elliptic system     

SOME PROPERTIES OF THE SOLUTION OF A FILTRATION PROBLEM IN PARTIALLY SATURATED POROUS MEDIA

A filtration problem with second initial-boundary value in partially saturated porous media isconsidered,In addition to discussion of the existence and uniqueness of weak solution of the problem,it is demonstrated that the interface between the saturated and unsaturated regions exists andcontinues under certain conditions and the solution possesses some properties,e.g.,the balance ofwater content,the time-limit existence of weak solution ect.,which differ from those of the solutionsof the first initial-boundary value problem.     

Nonlinear Hyperbolic-Parabolic System Modeling Some Biological Phenomena

In this paper, we study a nonlinear hyperbolic-parabolic system modeling some biological phenomena. By semigroup theory and Leray-Schauder fixed point argument, the local existence and uniqueness of the weak solutions for this system are proved. For the spatial dimension N = 1, the global existence of the weak solution will be established by the bootstrap argument.     

ON THE CAUCHY PROBLEM FOR AW-RASCLE SYSTEM WITH LINEAR DAMPING

The existence of global BV solutions for the Aw-Rascle system with linear damping is considered.In order to get approximate solutions we consider the system in Lagrangian coordinates,then by using the wave front tracking method coupling with and suitable splitting algorithm and the ideas of[1]we get a sequence of approximate solutions.Finally we show the convergence of this approximate sequence to the weak entropic solution.     

PIECEWISE SMOOTH SOLUTIONS OF SEMILINEAR HYPERBOLIC SYSTEMS IN HIGHER SPACE DIMENSION

This paper discusses piecewise smooth solutions for semilinear hyperbolic systems in multi-dimensional space. In the class of piecewise smooth functions the author proves the existence and uniqueness of local solutions to the Cauehy problem for 3×3 hyperbolic system. Besides, it is also proved that when two characteristic surfaces bearing weak singularities intersect, the solution will still be piecewise smooth and the weak singularities will propagate along all characteristic surfaces.     

THE SINGULARLY PERTURBED BOUNDARY VALUE PROBLEM OF NONLINEAR INTEGRO-DIFFERENTIAL SYSTEM

In this paper, using the differential inequality and singularly perturbed theory, the singularly perturbed boundary value problems for nonlinear integro-differential system has been studied. Under some appropriate assumptions, the existence of solution has been proved and the uniform validness of the asymptotic expansions for arbitrary nth-order have been obtained simply and conveniently.     

Results for a turbulent system with unbounded viscosities: Weak formulations,existence of solutions,boundedness and smoothness

We consider a circulation system arising in turbulence modelling in fluid dynamics with unbounded eddy viscosities. Various notions of weak solution are considered and compared. We establish existence and regularity results. In particular we study the boundedness of weak solutions. We also establish an existence result for a classical solution.     

A coupled system of integral equations in reflexive banach spaces

We present an existence theorem for at least one weak solution for a coupled system of integral equations of Volterra type in a reflexive Banach spaces relative to the weak topology.     

Blow-up result and energy decay rates for binary mixtures of solids with nonlinear damping and source terms

In this paper we study the long-time behavior of binary mixture problem of solids, focusing on the interplay between nonlinear damping and source terms. By employing nonlinear semigroups and the theory of monotone operators, we obtain several results on the existence of local and global weak solutions, and uniqueness of weak solutions. Moreover, we prove that every weak solution to our system blows up in finite time, provided the initial energy is negative and the sources are more dominant than the damping in the system. Additional results are obtained via careful analysis involving the Nehari Manifold. Specifically, we prove the existence of a unique global weak solution with initial data coming from the “good” part of the potential well. For such a global solution, we prove that the total energy of the system decays exponentially or algebraically, depending on the behavior of the dissipation in the system near the origin.     

Nonstationary nonlinear nonlocal problem of radiative–conductive heat transfer in a system of opaque bodies with properties depending on the radiation frequency

We consider a nonstationary nonlinear initial-boundary value problem governing radiative-conductive heat transfer in a periodic system of grey heat shields. The existence and uniqueness of a weak solution and a regular weak solution are established. Estimates for the solutions in terms of the data of the problem are obtained. Bibliography: 36 titles.     

Reproductive solution of a second-grade fluid system

We treat the existence and uniqueness of reproductive solution (weak time-periodic solution) of a second-grade fluid system for small enough source terms, by using the Galerkin approximation method and compactness arguments.     

Global weak solutions for a periodic two-component?μ-Hunter–Saxton system

This paper is concerned with global existence of weak solutions for a periodic two-component?μ-Hunter–Saxton system. We first derive global existence for strong solutions to the system with smooth approximate initial data. Then, we show that the limit of approximate solutions is a global weak solution of the two-component?μ-Hunter–Saxton system.     

Existence results for a class of degenerate quasilinear elliptic systems

We establish existence results for weak solutions of degenerate quasilinear elliptic systems. By using the variational method we obtain the existence of a solution for an elliptic system with Dirichlet boundary condition under some restriction on λ.     

向量拟平衡问题系统及其应用

引入了向量拟平衡问题系统并证明了其解的存在性定理．作为应用，还得到约束多目标对策和无约束多目标对策弱Pareto平衡的一些存在性结果．     

Existence of optimal controls for systems governed by parabolic partial differential equations with Cauchy boundary conditions

Summary This paper considers the existence of optimal controls for systems governed by a second order parabolic partial differential equation in divergence form with Cauchy conditions. As preliminary results, theorems concerning the convergence of the sequence of weak solutions corresponding to a sequence of admissible controls are proved. Two general forms of criteria are considered. The first one is taken as a function of the weak solution of the system, and the other is taken as a function of the solution of the system and control. Several theorems and corollaries on the existence of optimal controls are then presented.     

On the existence of finite energy weak solutions to the Navier–Stokes equations in irregular domains

This paper studies the existence of weak solutions of the Navier–Stokes system defined on a certain class of domains in ?³ that may contain cusps. The concept of such a domain and weak energy solution for the system is defined and its existence is proved. However, thinness of cusps must be related to the adiabatic constant appearing in the pressure law. Copyright © 2008 John Wiley & Sons, Ltd.