On the Dirichlet Problem for Quasi-linear Elliptic Equation with a Small Parameter

In this paper we deal with the Dirichlet problem for quasilinear ellipticequation with a small parameter at highest derivatives.In case the character-istics of the degenerated equation are curvilinear and the domain,where theproblem is defined,is a bounded convex domain,we offer a method to cons-truct the uniformly valid asymptotic solution of this problem,and prove thatthe solution of this problem really exists,and being uniquely determined asthe small parameter is sufficiently small.     

Analytical solution of basic equations set of atmospheric motion

On condition that the basic equations set of atmospheric motion possesses the best stability in the smooth function classes, the structure of solution space for local analytical solution is discussed, by which the third-class initial value problem with typicality and application is analyzed. The calculational method and concrete expressions of analytical solution about the well-posed initial value problem of the third kind are given in the analytic function classes. Near an appointed point, the relevant theoretical and computational problems about analytical solution of initial value problem are solved completely in the meaning of local solution. Moreover, for other type of problems for determining solution, the computational method and process of their stable analytical solution can be obtained in a similar way given in this paper.     

The solution of large deflection problem of thin circular plate by the method of composite expansion

In this paper, the method of composite expansion in perturbation theory is used for the solution of large deflection problem of thin circular plate. In this method. the outer field solution and the inner boundary layer solution are combined together to satisfy all the boundary conditions. In this paper, Hencky’s membrane solution is used for the first approximation in outer field solution, and then the second approximate solution is obtained. The inner boundary layer solution is found on the bases of boundary layer coondinate. In this paper, the reciprocal ratio of maximum deflection and thickness of the plate is used as the small parameter. The results of this paper improves quite a bit in comparison with the results obtained in 1948 by Chien Wei-zang.     

THE SOLUTION OF LARGE DEFLECTION PROBLEM OF THIN CIRCULAR PLATE BY THE METHOD OF COMPOSITE EXPANSION

In this paper, the method of composite expansion in perturbation theory is used for the solution of large deflection problem of thin circular plate. In this method. the outer field solution and the inner boundary layer solution are combined together to satisfy all the boundary conditions. In this paper, Hencky's membrane solution is used for the first approximation in outer field solution, and then the second approximate solution is obtained. The inner boundary layer solution is found on the bases of boundary layer coondinate. In this paper, the reciprocal ratio of maximum deflection and thickness of the plate is used as the small parameter. The results of this paper improves quite a bit in comparison with the results obtained in 1948 by Chien Wei-zang.     

ON THE UNIFORMLY VALID ASYMPTOTIC SOLUTION OF NON-LINEAR DIRICHLET PROBLEM

In this paper,Dirichlet problem for second order quasi-linear elliptic equation with a small parameter at highestderivatives is studied.In case degenerate equation has nosingular point and parameter εis sufficiently small,theexistence and uniqueness of solution are proved,and the uni-formly valid asymptotic solution is derived on the entire do-main.     

THE ANALYTICAL SOLUTION FOR HELMHOLTZ BOUNDARY PROBLEM IN NON-HORIZONTALLY STRATIFIED DOMAINS

There are N domains D_j.(j=0,1,……,N-1 )of different physical parameters in the whole space and their interfaces.S_(jj 1)are non-horizontally smooth curved surfaces.The following boundary problem is called Helmholtz boundary problem:The analytical solution of the above problem is given in this paper.     

New exact penalty function for solving constrained finite min-max problems

This paper introduces a new exact and smooth penalty function to tackleconstrained min-max problems.By using this new penalty function and adding justone extra variable,a constrained min-max problem is transformed into an unconstrainedoptimization one.It is proved that,under certain reasonable assumptions and when thepenalty parameter is sufficiently large,the minimizer of this unconstrained optimizationproblem is equivalent to the minimizer of the original constrained one.Numerical resultsdemonstrate that this penalty function method is an effective and promising approach forsolving constrained finite min-max problems.     

Boundary integral equations for the bending problem of plates on two-parameter foundation

By means of Fourier integral transformation of generalized fimction, the fimdamental solution for the bending problem of plales on two-parameter foundation is derived in this paper, and the fundamental solution is expanded into a uniformly convergent series.On the basis of the above work, two boundary integral eguations which are suitable to arhitrary shapes and arbitrary boundary conditions are established by means of the Rayleigh-Green identity. The content of the paper provides the powerful theories for the application of BEM in this problem.     

Life-span of classical solutions for one-dimensional hydromagnetic flow

The paper concerns Cauchy, problem for one-dimensional hydromagnetic dynamics with dissipative terms. When the dissipation coefficient is equal to zero it is shown that the smooth solutions develop shocks in the finite time if the initial amounts of entropy and magnetic field are smaller than those of sound waves; when it is larger than zero, and the initial amounts of entropy, this dissipation coefficient and the magnetic field in each period are smaller than those of sound waves, then the smooth solutions blow up in the finite time. Moreover, the life-span of the smooth solution is given.     

On the coupled vibration of an ideal fluid with a linear elastic structure

The purpose of this paper is to analyse theoretically and numerieally the coupled vibration of an ideal fiuid with a linear elastie structure.It is proved in the paper that the natural frequencies of the coupled vibration do exist and are all real positive. The paper presents an efficient method to transform a coupled fluid-structure system to the structure with added mass and the ribrational analysis of the former is replaced by the latter in vacuum only. Numerical solution is outlined for the transformed problem and a compact frequecy equation is derived in which fluid variables do not appear. This simplifies the analysis significanily. A convergent proof has been given to guarantee the reliability of the solution. The paper also offers a general algorithm combined with Ritz method, boundary element method, and finite element method to analyse the transformed problem. Based on this algorithm, one can apply a known structural analysing program, with a little modification, to solve many different kinds     

Progressing step by step and integrating calculation of overcritical deformation of spherical shallow shells

In this paper, the problem of second buckling of the spherical shallow shell is calculated by use of the method of progressing step by step and integrating. The result is more exact than that of first approximate analysis for over-critical deformation of spherical shallow shell. It has been solved that the solution of second approximate analysis in this problem can’t be found. The calculating example in this paper shows that the solution of progressing step by step and integrating converges to second approximate solution.     

Large deflection problem of a clamped elliptical plate subjected to uniform pressure

In this paper, the perturbation solution of large deflection problem of clamped elliptical plate subjected to uniform pressure is given on the basis of the perturbation solution of large deflection problem of similar clamped circular plate (1948), (1954). The analytical solution of this problem was obtained in 1957. However, due to social difficulties, these results have never been published. Nash and Cooley (1959) published a brief note of similar nature, in which only the case λ=a/b=2 is given. In this paper, the analytical solution is given in detail up to the 2nd approximation. The numerical solutions are given for various Poisson ratios v=0.25, 0.30, 0.35 and for various eccentricities λ=1, 2, 3, 4, 5, which can be used in the calculation of engineering designs.     

UNIFORM DIFFERENCE SCHEME FOR A SINGULARLY PERTURBED LINEAR 2ND ORDER HYPERBOLIC PROBLEM WITH ZEROTH ORDER REDUCED EQUATION

In this paper a singularly perturbed linear second order hyperbolic problem with zerothorder reduced equation is discussed.Firstly,an energy inequality of the solution and anestimate of the remainder term of the asymptotic solution are given.Then an exponentiallyfitted difference scheme is developed in an equidistant mesh.Finally,uniform convergencein small parameter is proved in the sense of discrete energy norm.     

Initial-boundary value problem of one class of nonlinear Schrödinger equations described in molecular crystals

In this paper, we study the initiial-boundary value problem of one class of nonlinear Schrodinger equations described in molecular crystals. Furthermore, the existence of the global solution is obtained by means of interpolation inequality and a priori estimation.     

Quadratic minimization for equilibrium problem variational inclusion and fixed point problem

The purpose of this paper is to find the solutions to the quadratic mini- mization problem by using the resolvent approach. Under suitable conditions, some new strong convergence theorems are proved for approximating a solution of the above min- imization problem. The results presented in the paper extend and improve some recent results.     

Reconstruction of high order derivatives by new mollification methods

In this paper, the problem of reconstructing numerical derivatives from noisy data is considered. A new framework of mollification methods based on the L generalized solution regularization methods is proposed. A specific algorithm for the first three derivatives is presented in the paper, in which a modification of TSVD, termed cTSVD is chosen as the regularization technique. Numerical examples given in the paper verify the theoretical results and show efficiency of the new method.     

THE SCHRDINGER EQUATION OF THIN SHELL THEORIES

This work is the continuation of the discussions of[50]and[51].In this paper:(A)The Love-Kirchhoff equation of small deflection problem for elastic thin shellwith constant curvature are classified as the same several solutions of Schr(?)dingerequation,and we show clearly that its form in axisymmetric problem;(B)For example for the small deflection problem,we extract the general solution ofthe vibration problem of thin spherical shell with equal thickness by the force in centralsurface and axisymmetric external field,that this is distinct from ref.[50]in variable.Today the variable is a space-place,and is not time;(C)The von Kármán-Vlasov equation of large deflection problem for shallow shellare classified as the solutions of AKNS equations and in it the one-dimensional problem isclassified as the solution of simple Schr(?)dinger equation for eigenvalues problem,and wetransform the large deflection of shallow shell from nonlinear problem into soluble linearproblem.     

THE ASYMPTOTIC SOLUTION OF A KIND OF STEFAN PROBLEM

In this paper,a kind of Stefan problem subject to general initial condition is studied.The slab considered is divided into three regions.There is a different time scale in each one.By means of PLK method or like multi-scales method,the asympto-tic solution of each one is obtained.Finally we discuss the asymptotic solution and draw some conclusions.     

PROGRESSING STEP BY STEP AND INTEGRATING CALCULATION OF OVERCRITICAL DEFORMATION OF SPHERICAL SHALLOW SHELLS

In this paper,the problem of second buckling of the spherical shallow shell is calculatedby use of the method of progressing step by step and in integating.The result is more exactthan that of first approximate analyis for over-critical deformation of spherical shallowshell It has been solved that the solution of second appoximate analysis in this problemcan’t befound.The calculating example in this paper shows that the solution of progressingstep by step and integrating converges to second approximate solution.     

Application of subregion function method for solving beam-board structure

In this paper,the solution to the structure consisting of a bead and a board is given as aresult of the application of the subregion function method which was suggested in ref.[1].The same problem is also computed with finite element method.The comparison betweenthe two results shows that the application of the subregion function in the method of weightedresiduals is practical and effective,especially for solving compound structures.