On the Asymptotic Property of Solutions to Some Nonlinear Dissipative Wave Equations

In this paper the decay of global solutions to some nonlinear dissipative wave equations are discussed, which based on the method of prior estimate technique and a differenece inequality.

Singular Perturbations for a Class of Fourth-order Nonlinear Boundary Value Problem

This paper is devoted to study the following the singularly perturbed fourth-order ordinary differential equation ∈y（4） =f（t,y＇,y＇＇,y＇＇＇）,0t1,0ε1 with the nonlinear boundary conditions y（0）=y＇（1）=0,p（y＇＇（0）,y＇＇＇（0））=0,q（y＇＇（1）,y＇＇＇（1））=0 where f：[0,1]×R3→R is continuous,p,q：R2→R are continuous.Under certain conditions,by introducing an appropriate stretching transformation and constructing boundary layer corrective terms,an asymptotic expansion for the solution of the problem is obtained.And then the uniformly validity of solution is proved by using the differential inequalities.

A Class of Nonlinear Singularly Perturbed Problems of Fourth Order

A class of fourth order singularly perturbed boundary value problems are studied. The existence of solution and its uniformly valid asymptotic estimation are obtained.

A Class of Singularly Perturbed Problems for Nonlinear Elliptic Equations

A class of singularly perturbed problems for the nonlinear elliptic equations is considered. Under suitable conditions, using the theory of differential inequalities the asymptotic behavior of solution for the boundary value problems are studied, which reduced equations possess two intersecting solutions.

The Singularly Perturbed Nonlinear Boundary Value Problem

The singularly perturbed nonlinear problem where y,f, A, B are n-dimensional vectors is considered. Under the appropriate assump- tions the authors prove that there exists a solution y(x, ) and the estimation of y(x,) is obtained using the method of differential inequalities.

A NEW REGULARITY CLASS FOR THE NAVIER-STOKES EQUATIONS IN IR^n

Consider the Navier-Stokes equations in IRn×(0, T), for n≥3. Let 1 < a≤min{2, n/(n-2)} and define β by (2/a)+ (n/β) = 2. Set α′= α/(α-1). It is proved that Dv belongs to C(0, T; Lα′) ∩ Lα′ (0, T; L2β/(n-2)) whenever Dv ∈ Lα(0, T; Lβ). In pwticular, v is a regular solution. This results is the natural extensinn to α ∈ (1, 2] of the classical sufficient condition that establishes that Lα(0, T; Lγ) is a regularity class if (2/α)+(n/γ) = 1. Even the borderline case α = 2 is significat. In fact, this result states that L2(0, T; W1,n) is a regularity class if n≤ 4. Since W1,n→L∞ is false, this result does not follow from the classical one that states that L2(0, T; L∞) is a regularity class.

Optimal concavity of some Hessian operators and the prescribed σ_2 curvature measure problem

In this paper, we consider a minimal value problem and obtain an algebraic inequality. As an application, we obtain the optimal concavity of some Hessian operators and then establish the C2 a priori estimate for a class of prescribed σ2 curvature measure equations.

HENIG GLOBALLY EFFICIENCY FOR SET-VALUED OPTIMIZATION AND VECTOR VARIATIONAL INEQUALITY

This paper deals with Henig globally efficiency in vector optimization involving generalized cone-preinvex set-valued mapping. Some properties of generalized cone-preinvex set-valued map are derived. It also disclose the closed relationships between Henig globally efficiency of generalized conepreinvex set-valued optimization problem and Henig globally efficiency of a kind of vector variational inequality.

Regularity of Keldys-Fichera Boundary Value Problem for Degenerate Elliptic Equations

The authors discuss the W1,p-solutions and the interior regularity of weak solutions for the Keldys-Fichera boundary value problem using the acute angle principle,the reversed Hlder inequality and the generalized poincar'e inequalities.

BILEVEL PROGRAMMING MODEL AND SOLUTION METHOD FOR MIXED TRANSPORTATION NETWORK DESIGN PROBLEM

By handling the travel cost function artfully, the authors formulate the transportation mixed network design problem （MNDP） as a mixed-integer, nonlinear bilevel programming problem, in which the lower-level problem, comparing with that of conventional bilevel DNDP models, is not a side constrained user equilibrium assignment problem, but a standard user equilibrium assignment problem. Then, the bilevel programming model for MNDP is reformulated as a continuous version of bilevel programming problem by the continuation method. By virtue of the optimal-value function, the lower-level assignment problem can be expressed as a nonlinear equality constraint. Therefore, the bilevel programming model for MNDP can be transformed into an equivalent single-level optimization problem. By exploring the inherent nature of the MNDP, the optimal-value function for the lower- level equilibrium assignment problem is proved to be continuously differentiable and its functional value and gradient can be obtained efficiently. Thus, a continuously differentiable but still nonconvex optimization formulation of the MNDP is created, and then a locally convergent algorithm is proposed by applying penalty function method. The inner loop of solving the subproblem is mainly to implement an Ml-or-nothing assignment. Finally, a small-scale transportation network and a large-scale network are presented to verify the proposed model and algorithm.

ＲＥＧＵＬＡＲＩＴＹ ＲＥＳＵＬＴＳ ＦＯＲ ＬＩＮＥＡＲＥＬＬＩＰＴＩＣ ＰＲＯＢＬＥＭＳ ＲＥＬＡＴＥＤＴＯ ＴＨＥ ＰＲＩＭＩＴＩＶＥ ＥＱＵＡＴＩＯＮＳ

The authors study the regularity of soutions of the GFD-Stokes problem and of some second order linear elliptic partial differential equations related to the PrimitiveEquations of the ocean .The present work generallizes the regularity results in[18] by taking into consideraion the non- homogeneous boundary conditions and teh dependence of solutions on the thickness of the domain occupied by the ocean and its varying bottom topography. These regularity results are important tools in the study of the PEs(see e.g.[6]), and they seem also to possess their own interest.

TRANSITION FROM A DEFLAGRATION TO A DETONATION IN GAS DYNAMIC COMBUSTION

The transition from a deflagration to a detonation (DDT) in gas dynamics is investigated through the process of a deflagration with a imite width flame overtaken by a shock. The problem is formulated as a free boundary value problem in an angular domain with a strong detonation and a reflected shock as boundaries. The main difficulty lies in the fact that the strength of reflected shock is zero at the vertex where the shock speed degenerates to be the same as the characteristic speed. The conclusion is that a strong detonation and a retonation (a reflected shock) form locally. Also the entropy satisfaction of this solution is presented.