MATHEMATICAL PROBLEMS ON THE FLUID-SOLUTE-HEAT FLOW THROUGH POROUS MEDIA Ⅱ. PARTIALLY SATURATED CASE

A degenerate parabolic system arising from the fluid-solute-heat flow through partiallysaturated porous media is considered. The existence of weak solutions to the initial boundary valueproblem of this system is established by time discretization, and the continuity of the weak solutionsis discussed.     

AN ELLIPTIC-PARABOLIC SYSTEM ARISING FROM THE FLUID-SOLITE-HEAT FLOW THROUGH SATURATED POROUS MEDIA

In this paper an elliptic-parabolic coupled system arising from the fluid-solute-heat flowthrough a saturated porous medium is considerd.The uniqueness and the existence of classicalsolutions are proved.The asymptotic behavior of solutions for large time is shown,too.     

THE BOUNDARY VALUE PROBLEMS FOR THE FILTRATION EQUATION IN PARTIALLY SATURATED POROUS MEDIA

In this paper we considered the first and the second boundary value problems for one-dimensionalfiltration in partially saturated porous media.The existence,uniqueness and regularity of weaksolutions were obtained.We also studied the interface problems and discussed the asymptotic behaviorof weak solutions.     

PLANE ELASTIC PROBLEMS OF DIFFERENT MEDIA WITH CRACKS ON THE INTERFACE

The equllibrium problem for the infinite elastic plane consisting of two different media with many cracks on the interface is discussed.It is transferred to a boundary value problem for analytic functions and then further reduced to a singular integral equation,the unique solvability and an effective method of solution for which are eatablished.A practical example in applications is illustrated,the solution of which is obtained in closed form.     

ON THE SINGULAR VARIATIONAL PROBLEMS

The authors deal with the singular variational problem S(a,b,λ0):=infu∈E,u(≡／)0 ∫RN(||X|-a(△)u|m ∫|x|-(a 1)m|u|m)dx/(∫RN||X|-bU|P dx)m/p as well as (S)=(S)(a,b,λ1,λ2):=u,ν,E∈,u(u,ν)(≡／)(1,1) ∫RN J(u,ν)dx/(∫RN|x|-bp|u|α|ν|βdx)m/p, whereJ(u, v) = ||x|- au|m λ1|x|- (a 1)m|u|m ||x|- av|m λ2|x|- (a 1)m|v|m,N ≥ m 1 ＞ 2, 0 ≤ a ＜ N-m/m, a ≤ b ＜ a 1 and p = p(a,b) = α β =Nm/N-m m(b-a), α, β≥ 1, E = D1,mα(RN). The aim of this paper is to show the existence of minimizer for S(a, b, A0) and S(a, b, λ1, λ2).     

ON THE BOTTLENECK CAPACITY EXPANSION PROBLEMS ON NETWORKS

This article considers a class of bottleneck capacity expansion problems. Such problems aim to enhance bottleneck capacity to a certain level with minimum cost. Given a network G(V, A, C) consisting of a set of nodes V= {v1,v2,…,vn},a set of arcs A ■ {(vi, vj) | i=1,2,…, n;j=1,2,…,n} and a capacity vector C. The component cij of C is the capacity of arc (vi ,vj). Define the capacity of a subset A' of A as the minimum capacity of the arcs in A, the capacity of a family F of subsets of A is the maximum capacity of its members. There are two types of expanding models. In the arc-expanding model, the unit cost to increase the capacity of arc (vi, vj) is wij. In the node-expanding model, it is assumed that the capacities of all arcs (vi,vj) which start at the same node vi should be increased by the same amount and that the unit cost to make such expansion is wi. This article considers three kinds of bottleneck capacity expansion problems (path, spanning arborescence and maximum flow) in both expanding models. For each kind of expansion problems, this article discusses the characteristics of the problems and presents several results on the complexity of the problems.     

ON THE MULTIPLICATIVE INVERSE EIGENVALUE PROBLEMS

We present new sufficient conditions on the solvability and numerical methods for the following multiplicative inverse eigenvalue problem: Given an n x n real matrix A and n real numbers λ1 , λ2,..., λn, find n real numbers c1, c2,..., cn such that the matrix diag(c1,c2,...,cn)A has eigenvalues λ1,λ2,..., λn.     

THE INFILTRATION PROBLEM WITH CONSTANT RATE IN PARTIALLY SATURATED POROUS MEDIA

In the present paper we study the infiltration problem with constant rate in partially saturatedporous media.The main results are:(i)There exists an unique weak solution to the infiltration problemwith two degenerate situations.(ii)When the infiltration rate is not large enough,the partiallysaturated state will fall down to completely unsaturated state with the increase of time.     

ON THE COUPLING METHODS FOR COUPLED PROBLEMS

The coupled problem means fluid-structure interaction widely encountered in aviation, offshore and nuclear engineerings. The coupling method here means the combination of finite and boundary elements(FE/BE)to improve the computational effciency considerably. In this paper, a general math. Model for simulation of the wetted structure dynamic response to inter/external fluid flow is presented. In particular, the various boundary conditions for fluid region are treated sophsticatodiy. In this way, only the displacement and pressure remain to be the independent variables so that both computer cost and accuracy could be improved. The FORTRAN program package of this model has been compiled on #Univac-1110 in Madison (MACC), USA, and on #M340S computer in Wuhan University, China. As a first approximation, in this paper a 2-D example for the ship-wave interaction analysis is illustrated.     

SOME BOUNDARY PROBLEMS OF THE SPIN SYSTEMS AND THE SYSTEMS OF FERRO-MAGNETIC CHAIN Ⅰ. NONLINEAR BOUNDARY PROBLEMS

§1. Introduction The nonlinear system of partial differential equations and the corresponding system with diffusion term are interesting and meaningful both in physical and mathematical point of view, where z= (u, v, w) and f(x, t, z) are two three-dimensional vector functions and"× "denotes the cross product operator of two three-dimensional vectors. The system (1) contains the so-called Landau- Lifschitz equation of isotropic Heigenberg ferro-magnetio chain as the     

ON THE COMPLETENESS OF THE GENERALIZED AXISYMMETRIC STOKES FLOW EQUATION

This paper defines new kinds of functions——the conjugate axisymmetric poteptial functions. With the aid of them, we can prove the completeness of the solutions of the generalized axisymmetric Stokes flow equation without the condition on the convexity of the domain.     

ON THE REGULARITY OF THE MINIMUM SOLUTION OF THE RESTRAINED VARIATIONAL PROBLEMS

This paper is concerned with the regularity of minimum solution u of the following functional on the restraint Under appropriate conditions, the bounded minimum solution u of the above functional is proved to be nothing but Hlder continuous.     

THE MATHEMATICAL PROBLEMS OF COMPOUND MATERIALS WITH CRACKS IN PLANE ELASTICITY

The problems of fracture of compound materials are very important in practical applications. In case of infinite plane, when the interface is a straight line and the cracks are rectilinear, there were many investigations     

ON THE DIRICHLET PROBLEMS OF DOUBLY-PERIODIC ANALYTIC FUNCTIONS

Let Im(ω_2/ω_1)>0 and S_0 be the parallelogram with vertices ±ω_1±ω_2 (the fundamental cell). Let L_0 be a closed smooth curve in So with the counterclockwise sense as its positive direction which bounds a region S_0~+ Denote     

THE ERGODICITY OF STOCHASTIC GENERALIZED POROUS MEDIA EQUATIONS WITH LVY JUMP

In this article,we first prove the existence and uniqueness of the solution to the stochastic generalized porous medium equation perturbed by Lévy process,and then show the exponential convergence of(pt)t≥0 to equilibrium uniform on any bounded subset in H.     

ON THE MODIFICATIONS OF CLASSICAL ORTHOGONAL POLYNOMIALS: THE SYMMETRIC CASE

We consider the modifications of the monic Hermite and Gegenbauer polynomials via the addition of one point mass at the origin. Some properties of the resulting polynomials are studied ; three-term recurrence relation, differential equation, ratio asymptotics, hypergeometric representation as well as, for large n, the behaviour of their zeros.     

THE INFILTRATION PROBLEM WITH LARGE CONSTANT SURFACE FLUX IN PARTIALLY SATURATED POROUS MEDIA

Infiltration problem with two kinds of degenerate cases is considered.After proving the existenceof weak solution,we study when water content c(u(·,t))has compact support and how the solutionbehaves as t→∞.Moreover,we get existence and regularity of two kinds of free boundaries undersome conditions on the initial date.     

ON CRACK PROBLEMS IN AN INFINITE PLANE CONSISTING OF THREE DIFFERENT MEDIA

The mathematical problem of an infinite elastic plane consisting of three different media with an arbitrary number of cracks is considered. It is reduced to singular integral equations along the interfaces and the cracks by a constructive method. Those along the interfaces are further reduced to Fredholm ones.