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.     

THE LATERAL BOUNDARY OF THE SUPPORT OF WEAK SOLUTIONS OF THE FILTRATION EQUATION IN ONE DIMENSION

<正> §0. INTRODUCTION In the present paper we shall consider a flow of water through a homogeneous isotropicrigid porous medium. Let function u(x, t) denote the volumetric moisture content, which isdefined locally as the volume of water per unit volume of the porous medium, and q the seepage velocity which is defined locally as the volume of water flowing across unit area of the     

A NOTE ON THE SOLUTION TO NEUMANN BOUNDARY VALUE PROBLEM OF SECOND ORDER NONLINEAR DIFFERENTIAL EQUATION

The author of this paper, by means of the semi-rank theory, establish a new comparative theorem and give the existence of maximal and minimal solutions to Neumann boundary value problems of second order nonlinear differential equation in ordered Banach spaces when the upper and lower solutions in the reversed order of the problem are given.     

ON THE TRANSPORT EQUATION WITH INTEGRAL BOUNDARY CONDITIONS AND ITS CONSERVAIVE LAW

The well-posedness for the time-dependent neutron transport equationwith integral boundary conditions is established in L~1 space. Some spectral propertiesof the transport operator are discussed, the dominant eigenvalue is proved existing,and furthermore, the conservative law of migrating particle numbers is established.     

THE SINGLE-POINT QUENCHING OF NONLINEAR DEGENERATE FUNCTIONAL REACTION-DIFFUSION EQUATION

This article is concerned with the quenching phenomena of the nonlinear degenerate functional reaction-diffusion equation. Some results are obtained on the single-point quenching and the uniqueness of quenching.     

ON THE RELATIVISTIC BOLTZMANN EQUATION

1IntroductionWearecollcernedwithglobalealstellceofsolutionsoftheinitialvalueproblelllfortherelativisticBoltzlllallnequation(orinbrief,RBE)[1]wilersthedifferelltpartsareexplailledbelow.cp=(t,x)alldpl'=(po,p)respectivelyrepresentafour-dinlellsiollalspace-timedinlensionlessvariablealldafour--dimellsionalulolllentum-energydimensionlessvariable.f=f(t,x,p)isadistributiollf'llllctiollofaolle-particleclassicalrelativisticgaswithoutexterllalforces.W(P,pl;p',pl)isatrallsitiollratewhichdepelldsonlyonti…     

ON THE EQUIVALENCE OF THE ABEL EQUATION

This article uses the reflecting function of Mironenko to study some complicated differential equations which are equivalent to the Abel equation. The results are applied to discuss the behavior of solutions of these complicated differential equations.     

ON THE EXISTENCE OF SOLUTIONS TO A BI-PLANAR MONGE-AMPèRE EQUATION

In this article, we consider a fully nonlinear partial differential equation which can be expressed as a sum of two Monge-Ampère operators acting in different two-dimensional coordinate sections. This equation is elliptic, for example, in the class of convex functions.We show that the notion of Monge-Ampère measures and Aleksandrov generalized solutions extends to this equation, subject to a weaker notion of convexity which we call bi-planar convexity. While the equation is also elliptic in the class of bi-planar convex functions, the contrary is not necessarily true. This is a substantial difference compared to the classical Monge-Ampère equation where ellipticity and convexity coincide. We provide explicit counter-examples: classical solutions to the bi-planar equation that satisfy the ellipticity condition but are not generalized solutions in the sense introduced. We conclude that the concept of generalized solutions based on convexity arguments is not a natural setting for the bi-planar equation.     

ON THE EXISTENCE OF ALMOST GLOBAL WEAK SOLUTION TO MULTIDIMENSIONAL VLASOV-POISSON EQUATION

§１．ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｉｄｅｒｔｈｅｆｏｌｏｗｉｎｇｄｄｉｍｅｎｓｉｏｎａｌＶｌａｓｏｖＰｏｉｓｏｎｓｙｓｔｅｍ，ｄ＝２，３，ｔｆ＋ｖ·ｘｆ－Ｅ·ｖｆ＝０，ｆ（０，ｘ，ｖ）＝ｆ０（ｘ，ｖ），Ｅ（ｔ，ｘ）＝ｃ（ｄ）∫ｘ－ｙ｜ｘ...     

DIRICHLET PROBLEMS FOR MONGE-AMPERE EQUATION DEGENERATE ON BOUNDARY

The existence of C~∞ -solutions to Dirichlet problem for Monge-Ampere equation degenerate on boundary is proved, and some applications to the equation prescribed Gaussian curvature are also given.     

ON THE EXISTENCE OF PERIODIC SOLUTIONS TO CERTAIN FOURTH ORDER DIFFERENTIAL EQUATION

ＯＮＴＨＥＥＸＩＳＴＥＮＣＥＯＦＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＳＴＯＣＥＲＴＡＩＮＦＯＵＲＴＨＯＲＤＥＲＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＦｅｎｇＣｈｕｎｈｕａ（冯春华）（ＧｕａｎｇｘｉＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，广西师范大学，邮编：５...     

THE WELL-POSEDNESS OF THE ABSTRACT KINETIC EQUATION BOUNDARY VALUE PROBLEMS

In this paper the abstract boundary value problem on Hilbert space H is studied: where Q /Q- are the maximum positive/negative spectral projections of self-adjoint operator T. Under suitable conditions, it is shown that the boundary value problem of abstract kinetic equation is well-posed and can be applied to transport theory.     

THE EQUIVALUED BOUNDARY VALUE PROBLEMS FOR THE MINIMAL SURFACE EQUATION

There has been a long history on the study of the minimal surface equation (see [1]—[3]), For a tightly stretched uniform membrane in balance, its place can be discribed by the minimal surface equation. In this paper we will discuss boundary value problems of the minimal surface equation with equivalued boundary conditions on a complex connected domain. The physical meaning of such pro-     

THE EQUIVALUED BOUNDARY VALUE PROBLEMS FOR THE MINIMAL SURFACE EQUATION

There has been a long history on the study of the minimal surface equation(see[1]—[3]).For a tightly stretched uniform membrane in balance,its place can be discribed by the minimal surface equation.In this paper we will discuss boundary value problems of the minimal surface equation with equivalued boundary conditions on a complex connected domain.The physical meaning of such problems will be given later. The linear approximation of the minimal     

THE BOUNDARY VALUE PROBLEMS OF ELLIPTICSYSTEM (E_1) ON THE UNBOUNDED DOMAIN

1 IntroductionIn [1]. Hua, Lin and Wu developed a fullction tlieory of (A, k) bianalytic functions byinvestigatiug the second order systems of equations on the plalle. Long after a decade, it comesto know that biaualytic functions are related essentially and closely to plane elasticity. Upon80s. Gilbert and Li.[2] firstly brouglit sucli a relation to llglit. ln fact, tl1eir observation showstl1at tl1e canoliical fOrlll of tl1e elliptic systelll (E1) ili [1], wliicl1 is satisfied by (A, 1)-…     

BLOW-UP AT THE BOUNDARY FOR DEGENERATE DIFFUSION EQUATION

ＢＬＯＷ－ＵＰＡＴＴＨＥＢＯＵＮＤＡＲＹＦＯＲＤＥＧＥＮＥＲＡＴＥＤＩＦＦＵＳＩＯＮＥＱＵＡＴＩＯＮ￥ＣａｏＺｈｅｎｃｈａｏ（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＸｉａｍｅｎＵｎｉｖ．Ｘｉａｍｅｎ３６１００５）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐｅｒｃｏｎｓｉ...     

ON THE DISCRETE-ORDINATES METHOD FOR THE MONOENERGETIC NEUTRON TRANSPORT EQUATION IN A SLAB WITH GENERALIZED BOUNDARY CONDITIONS

This paper is devoted to discussing the discrete-ordinates method for the monoenergetic neutron transport equation in a slab with generalized boundary conditions. For homogeneous medium with isotropic scattering and fission, the convergence theorems for discrete-ordinates approximations are given respectively for critical eigenvalue problem and dominant eigenvalue problems: for inhomogeneous medium with anisotropic scattering and fission, a similar discussion and an estimation for the convergence rate are given for critical eigenvalue problems. Finally, some numerical results are given by use of this method.     

NEW RESULTS ON THE EXISTENCE OF PERIODIC SOLUTIONS TO LINARD EQUATION

In this paper, a Liénard equation with a deviating argument has been studied by means of Mawhin's continuation theorem. A new result guaranteeing the existence of periodic solutions is obtained.     

NOTE ON A BOUNDARY VALUE PSOBLEM OF POISSON''''S EQUATION

ＮＯＴＥＯＮＡＢＯＵＮＤＡＲＹＶＡＬＵＥＰＳＯＢＬＥＭＯＦＰＯＩＳＳＯＮ＇ＳＥＱＵＡＴＩＯＮ￥ＦＥＮＧＣＨＡＯＫＥＮＧ；ＨＳＵＬＩＺＨＩ；ＡＮＤＹＵＨＯＮＧＱＵＡＮＡｂｓｔｒａｃｔ：ＴｈｉｓｎｏｔｅｓｈｏｗｓｔｈａｔｆｏｒａＢＶＰｏｆＰｏｉｓｓｏｎ＇...     

THE NEW BOUNDARY LAYER EQUATION OF NON-NEWTONIAN FLUID FLOWS

The concept of a Boundary Layer, as a region adjacent to a solid boundary in which vorticity varies rapidly as a result of viscous convection and diffusion,outside of which the vorticity is zero, was introduced by prandlt, Some authors have made attempts to extend