应用数学和力学

1986 Vol. 7, No. 12

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Dissipation Mechanics and Exact Solutions for Nonlinear Equations of Dissipative Type——Principle and Application of Dissipation Mechanics(I)

Shen Hui-chuan

1986, 7(12): 1061-1075.

Abstract(2078) PDF(664)

Abstract:
This work is the continuation and the distillation of the discussion of Refs. [1-4].(A) From complementarity principle we buildup dissipation mechanics in this paper. It is a dissipative theory of correspondence with the quantum mechanics. From this theory we can unitedly handle problems of macroscopic non-equilibrium thermodynamics and viscous hydrodynamics, and handle each dissipative and irreversible problems in quantum mechanics. We prove the basic equations of dissipation mechanics to eigenvalues equations of correspondence with the Schrodinger equation or Dirac equation in this paper.(B) We unitedly merge the basic nonlinear equations of dissipative type, especially the Navier-Stokes equation as a basic equation for macroscopic non-equilibrium thermodynamics and viscous hydrodynamics into integrability condition of basic equation of dissipation mechanics. And we can obtain their exact solutions by the inverse scattering method in this paper.

Studies on Bihypergeometric Equation

Wang Shen-xing

1986, 7(12): 1077-1090.

Abstract(1624) PDF(607)

Abstract:
This paper is offered to introduce a new differential equation, bihypergeometric equation, and to give its solutions.

The Stability of Zero Solution of Second Order System of Variable Coefficients with Four Non-Linear Terms

Zhong Hong-fa

1986, 7(12): 1091-1094.

Abstract(1721) PDF(635)

Abstract:
This paper discusses the following non-linear syste ms of second order coefficients: This paper is the generalization of works[1] and [2].

The Method of Transformation of the Boundaries for Forming the Permissible Displacements

Fu Bao-lian

1986, 7(12): 1095-1106.

Abstract(1658) PDF(657)

Abstract:
In this paper the method of transformation of the boundaries for structure the admissible displacements with various boundary conditions is presented. What is called the method of transformation of the boundaries is that, first we transform the actual system into the basic system and additional boundary forces and displacements on the basis of the superposition principle, then apply variational principles to the basic system, finally find the permissible displacement of the actual system by means of the method of transformation of the series.In this paper, we also give mixed energy principles under v iriation of boundary conditions. The mixed energy principles as the potential and complementary energy principles under variation of boundary conditions are all the chief theoretical fundamental of the method of transformation of the boundaries.Applying the method of transformation of the boundaries, we form the permissible displacements of rectangular plates of plane stress and bending problems with various edge conditions.Because the method of transformation of the boundaries is in progress to follow the variational principles and definite program to form permissible displacements, the difficulty in supposing and piecing together permissible displacements in the Rayleigh-Ritz method will be overcome.

Random Directional Contractors and Their Applications

Ding Xie-ping

1986, 7(12): 1107-1120.

Abstract(1571) PDF(476)

Abstract:
In this paper, as the generalizations of Altman's directional contractors^[4,5] and Lee and Padgett's random contractors^[1,2] we introduce the concept of random directional contractors for set-valued random operators. Using the new concept and transfinite induction, we show several existence theorems to solutions of nonlinear set-valued random operator equations. Our theorems improve and generalize the corresponding results in [1,2,4,5,11]. Next, some applications of our results to nonlinear random integral and differential equations are given.

On Singular Perturbation Boundary-Value Problem of Coupling Type System of Convection- Diffusion Equations

Yang Dan-ping

1986, 7(12): 1121-1132.

Abstract(1848) PDF(510)

Abstract:
In this paper we consider the singular perturbation boundary-value problem of the following coupling type system of convection-diffusion equations We advance two methods: the first one is the initial value solving method, by which the original boundary-value problem is changed into a series of unperturbed initial-value problems of the first order ordinary differential equation or system so that an asymptotic expansion is obtained;the second one is the boundary-value solving method, by which the original problem is changed into a few boundary-value problems having no phenomenon of boundary-layer so that the exact solution can be obtained and any classical numerical methods can be used to obtain the numerical solution ofconsismethods can be used to obtain the numerical solution of consistant high accuracy with respect to the perturbation parameter ε.

The Studies of Finite Supercavitating Airfoil

Lian Guang-chang

1986, 7(12): 1133-1150.

Abstract(1528) PDF(485)

Abstract:
An aerofoil above which is built the artificial cavity low pressure region is called "cavitating airfoil". By using generalized Blasius's theorem and conformal transformation, this paper investigates the problem of the flow past the aerofoil of cavitating airfoil with the Jetstream above cavitation, and gives the formulae of the lift and thrust.