PARAMETER IDENTIFICATION PROBLEM FOR A CLASS OF DISTRIBUTION PARAMETER SYSTEMS

The inverse parameter problem of the permeable law for the fracture reservoir with double poros'ty is of great importance in the exploitation of oil or gas. The total compressibility and permeability are the unknown geological parameters in the fluid motion equations. In this paper we discuss the inverse parameter problem from the point of the parameter identification of distributed parameter systems. We have considered solvability of the fluid motion equations with non-homogenous boundary value by the linear operator semi-group method, and have obtained the necessary conditions for the parameter identifiability.     

ASYMPTOTIC CONVERGENCE OF A GENERALIZED NON-NEWTONIAN FLUID WITH TRESCA BOUNDARY CONDITIONS

The goal of this article is to study the asymptotic analysis of an incompressible Herschel-Bulkley fluid in a thin domain with Tresca boundary conditions. The yield stress and the constant viscosity are assumed to vary with respect to the thin layer parameter ε.Firstly, the problem statement and variational formulation are formulated. We then obtained the existence and the uniqueness result of a weak solution and the estimates for the velocity field and the pressure independently of the parameter ε. Finally, we give a specific Reynolds equation associated with variational inequalities and prove the uniqueness.     

(2+1)维破裂孤子方程及Kadomtsev-Petviashvili方程的Stable-range解法(英文)

By using Xu’s stable-range method,families of explicit exact solutions with multiple parameter functions for the(2+1)-dimensional breaking soliton and KadomtsevPetviashvili equations.These parameter functions make our solutions more applicable to related practical models and boundary value problems.     

Boundary Shape Control of the Navier-Stokes Equations and Applications

In this paper, the geometrical design for the blade's surface in an impeller or for the profile of an aircraft, is modeled from the mathematical point of view by a boundary shape control problem for the Navier-Stokes equations. The objective function is the sum of a global dissipative function and the power of the fluid. The control variables are the geometry of the boundary and the state equations are the Navier-Stokes equations. The Euler-Lagrange equations of the optimal control problem are derived, which are an elliptic boundary value system of fourth order, coupled with the Navier-Stokes equations. The authors also prove the existence of the solution of the optimal control problem, the existence of the solution of the Navier-Stokes equations with mixed boundary conditions, the weak continuity of the solution of the Navier-Stokes equations with respect to the geometry shape of the blade's surface and the existence of solutions of the equations for the Gateaux derivative of the solution of the Navier-Stokes equations with respect to the geometry of the boundary.     

A numerical algorithm for determination of a control parameter in two-dimensional parabolic inverse problems

Numerical solution of the parabolic partial differential equations with an unknown parameter play a very important role in engineering applications. In this study we present a high order scheme for determining unknown control parameter and unknown solution of two-dimensional parabolic inverse problem with overspecialization at a point in the spatial domain. In this approach, a compact fourth-order scheme is used to discretize spatial derivatives of equation and reduces the problem to a system of ordinary differential equations(ODEs).Then we apply a fourth order boundary value method to the solution of resulting system of ODEs. So the proposed method has fourth order of accuracy in both space and time components and is unconditionally stable due to the favorable stability property of boundary value methods. The results of numerical experiments are presented and some comparisons are made with several well-known finite difference schemes in the literature.Also we will investigate the effect of noise in data on the approximate solutions.     

ON A CLASS OF SINGULAR INTEGRAL EQUATIONS WITH T ANSLATIONS

In this paper,singular integral equations with upper and lower translations arediscussed and the equivalence for solving them in and are shown.Equations with asingle pair of upper and lower translations are studied in detail.Their solutions as wellas the conditions of solvability are obtained.The method used consists of transferringthem to boundary value problems of analytic functions in upper and lower half-planesand then solving the latter.     

Fold completeness of a system of root vectors of a system of unbounded polynomial operator pencils in Banach spaces. II. Application

This paper is a continuation of the author’s paper in 2009,where the abstract theory of fold completeness in Banach spaces has been presented.Using obtained there abstract results,we consider now very general boundary value problems for ODEs and PDEs which polynomially depend on the spectral parameter in both the equation and the boundary conditions.Moreover,equations and boundary conditions may contain abstract operators as well.So,we deal,generally,with integro-differential equations,functional-differential equations,nonlocal boundary conditions,multipoint boundary conditions,integro-differential boundary conditions.We prove n-fold completeness of a system of root functions of considered problems in the corresponding direct sum of Sobolev spaces in the Banach Lq-framework,in contrast to previously known results in the Hilbert L 2-framework.Some concrete mechanical problems are also presented.     

Vanishing viscosity limits for the free boundary problem of compressible viscoelastic fluids with surface tension

We consider the free boundary problem of compressible isentropic neo-Hookean viscoelastic fluid equations with surface tension. Under the physical kinetic and dynamic conditions proposed on the free boundary, we investigate the regularity of classical solutions to viscoelastic fluid equations in Sobolev spaces which are uniform in viscosity and justify the corresponding vanishing viscosity limits. The key ingredient of our proof is that the deformation gradient tensor in Lagrangian coordinates c...     

THE ASYMPTOTIC BEHAVIOR OF SOLUTION FOR A CLASS OF STRONGLY NONLINEAR NON-AUTONOMOUS EQUATION

In this paper, using the singularly perturbed theory and the boundary layer corrective method, the asymptotic behavior of solution for a class of strongly nonlinear non-autonomous equations and the infection for asymptotic behavior of the solution with regard to the boundary condition are studied. According to the different regions of the boundary value, the asymptotic expansions of the solution for the original problem are obtained simply and conveniently.     

THE BOUNDARY VALUE PROBLEMS FOR QUASILINEAR HIGHER ORDER ELLIPTIC EQUATIONS WITH A SMALL PARAMETER

In this paper we deal with the general boundary value problems for quasilinear higherorder elliptic equations with a small parameter before higher derivatives.By using themethod of multiple scales,we have proved that if the solution of degenerated boundary valueproblem exists,then under certain assumptions as the small parameter is sufficiently small,the solution of the origional boundary value problem exists as well and it is unique in a certainfunction space.Besides,the asymptotic expansion of the solution has been constructed.     

THE SINGULAR LIMIT OF SECOND-GRADE FLUID EQUATIONS IN A 2D EXTERIOR DOMAIN

In this paper, we consider the second-grade fluid equations in a 2D exterior domain satisfying the non-slip boundary conditions. The second-grade fluid model is a wellknown non-Newtonian fluid model, with two parameters: α, which represents the length-scale,while ν > 0 corresponds to the viscosity. We prove that, as ν, α tend to zero, the solution of the second-grade fluid equations with suitable initial data converges to the one of Euler equations, provided that ν = o(α^4/3). Moreo...     

ON DOUBLY-PERIODIC RIEMANNIAN BOUNDARY VALUE PROBLEMS ALONG OPEN ARCS

In this paper, we consider the doubly-periodio Riemannian boundary value pro- blems (1.1) along a set L of smooth open arcs, any two of which are congruent to each other with respect to the two periods. In (1.1), G(t) ≠0 and g(t) are given functions on L, continuons in Holder and sense doubly-periodio, and \[{\Phi ^ \pm }(t)\] are the boundary values of the unknown doubly-periodio analytic function \[\Phi (z)\] along the different sides of L. Such problems are solved effectively so that both the solutions and the conditions of solvability are obtained in explicit forms. The results are then applied to solving certain classes of singular integral equations like (4.1) and (4,5) with kernels involving Weierstrass \[\xi \] functions. The case in which the two ends of each arc are congruent is also considered and similarly solved.     

POSITIVE SOLUTIONS TO A NONHOMO- GENEOUS NONAUTONOMOUS SECOND- ORDER BOUNDARY VALUE PROBLEM

The existence of multiple positive solutions is studied for a nonlinear nonauto- nomous second-order boundary value problem with nonhomogeneous boundary con- ditions. In order to describe the growth behaviors of nonlinearity on some bounded sets, two height functions are introduced. By considering the integrals of the height functions and applying the Krasnosel＇skii fixed point theorems on a cone, several new results are proved.     

NONSMOOTH CRITICAL POINT THEOREMS AND ITS APPLICATIONS TO QUASILINEAR SCHRDINGER EQUATIONS

In this paper, the existence and nonexistence of solutions to a class of quasilinear elliptic equations with nonsmooth functionals are discussed, and the results obtained are applied to quasilinear Schr¨odinger equations with negative parameter which arose from the study of self-channeling of high-power ultrashort laser in matter.     

Analytic Study of Magnetohydrodynamic Flow and Boundary Layer Control Over a Wedge

A genuine variational principle developed by Gyarmati, in the field of thermodynamics of irreversible processes unifying the theoretical requirements of technical, environmental and biological sciences is employed to study the effects of uniform suction and injection on MHD flow adjacent to an isothermal wedge with pressure gradient in the presence of a transverse magnetic field. The velocity distribution inside the boundary layer has been considered as a simple polynomial function and the variational principle is formulated. The Euler-Lagrange equation is reduced to a simple polynomial equation in terms of momentum boundary layer thickness. The velocity profiles, displacement thickness and the coefficient of skin friction are calculated for various values of wedge angle parameter m, magnetic parameter ξ and suction/injection parameter H. The present results are compared with known available results and the comparison is found to be satisfactory. The present study establishes high accuracy of results obtained by this variational technique.     

BOUNDARY LAYER ASYMPTOTIC BEHAVIOR OF INCOMPRESSIBLE NAVIER-STOKES EQUATION IN A CYLINDER WITH SMALL VISCOSITY

The object of this article is to study the boundary layer appearing at large Reynolds number （small viscosity ε） incompressible Navier Stokes Equation in a cylinder in space dimension three. These are Navier-Stokes equations linearized around a fixed velocity flow： the authors study the convergence as ε →0 to the inviscid type equations, the authors define the correctors needed to resolve the boundary layer and obtain convergence results valid up to the boundary and the authors also study the behavior of the boundary layer when, simultaneously, time and the Reynolds number tend to infinity, in which case the boundary layer tends to pervade the whole domain.     

RIEMANN-HILBERT PROBLEMS OF DEGENERATE HYPERBOLIC SYSTEM

This paper is concerned with the Riemann-Hilbert problems of degenerate hyperbolic system in two general domains, where the boundary curves are given by the parameter equations of the arc length s. We prove the existence and uniqueness of solutions to the Riemann-Hilbert problems by conformal deformations. The corre-sponding representations of solutions to the problems are also presented.     

PARAMETER IDENTIFICATION FOR THE DOUBLE POROSITY SYSTEMS IN FRACTURE RESERVOIRS

The inverse parameter problem of the permeable law of the naturally fractured reservoirs with double perosity is of great importance in the exploitation of oil The coefficients in the fluid motion equations are unknown geological parameters. In this paper, the history of matching problem of reservoir systems with double porosity has been discussed from the point of view of the parameter identification of distributed parameter systems, and the problems of identifiability and observability for this system are also dealt with. We have obtained the formulas of Fréchet derivative of the index functional in the identification parameters. These formulas are necessary for calculating identification parameters by a gradient or conjugate gradient method. The conditions of identifiability and observability for the reservoir system with double porosity are given.     

Global regularity for a class of Monge-Ampère type equations

In this paper we are concerned with the global regularity of solutions to the Dirichlet problem for a class of Monge-Ampère type equations.By employing the concept of(a,η) type domain,we emphasize that the boundary regularity depends on the convexity of the domain in nature.The key idea of our proof is to provide more effective global H?lder estimates of convex solutions to the problem based on carefully choosing auxiliary functions and constructing sub-solutions.     

BOUNDARY LAYER AND VANISHING DIFFUSION LIMIT FOR NONLINEAR EVOLUTION EQUATIONS

In this paper, we consider an initial-boundary value problem for some nonlinear evolution equations with damping and diffusion. The main purpose is to investigate the boundary layer effect and the convergence rates as the diffusion parameter α goes to zero.