MATHEMATICAL PROBLEMS ON THE FLUID-SOLUTE-HEAT FLOW THROUGH POROUS MEDIA Ⅰ. UNSATURATED CASE

A degenerate parabolic system arising from the fluid-solute-heat flow through unsaturatedporous media is considered. The existence of weak solutions to the initial boundary value problemof this system is esteblished by parabolic regularizaton. The regularity is proved as well, i. e. theweak solutions satisfy the equations and initial boundary conditions pointwise in the region wherethe moisture content is positive.     

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.     

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.     

FILTRATION IN PARTIALLY SATURATED AND PARTIALLY DRIED LAYERED POROUS MEDIA

1.IntroductionThefiltrationprobleminInferedporousmediaarisesfromthestudiesofwatermovementduringirrigationandofthesalinizationofsoil.Thisproblemhasbeenelaboratelyinvestigatedforthesaturatedcase,whileforthegeneralcase,worksseemtoconcentrateonlyonexperimentalandnumericalaspects.Theseworksrevealsomeinterestingtheoreticalquestions.FOrexample,HillandParlange[2]foundin1972thattheverticalinfiltrationofwaterintwo-layeredsandconstitutedwithfinerupperlayerandcoarserlowerisunstable.Afterthemathematicali…     

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.     

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.     

ONE DIMENSIONAL FILTRATION PROBLEM IN PARTIALLY SATURATED LAYERED POROUS MEDIA

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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.     

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 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.     

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.     

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 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 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     

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.     

THE ROTATION NUMBER AND DIRECTION OF A CONTINUOUS FLOW ON THE TORUS

In this paper the rotation direction r_f and rotation number p_f for any continuous flowon the torus are defined by applying Weil's theorem proved by Markley.The followingresults are obtained:(i)r_f=0 iff all orbits of f are proper and each limit set of f is homotopic to zeo onT~2;(ii)if r_f≠0,then p_f is irrational iff f has at least one non-trivial P stable orbit,p_f isrational iff f has at least one non-zero-homotopic closed or singular closed orbit.Then a method of computing the rotation number of certain flows is given.     

A NOTE ON THE STRONG CONSISTENCY OF ESTEMATES IN PARTIALLY LINEAR MODELS

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