UNIQUENESS FOR THE SOLUTIONS OF ELASTIC THIN PLATES AND SHALLOW SHELLS AS WELL AS THEIR CONTACT PROBLEM WITH HALF SPACE

The uniqueness for the solutions mentioned in the subject is proved by using the uniqueness of the solution for the internal boundary problem of Laplace and bi-Laplace equations of the first kind as well as of the second.

Uniqueness for the Linear Theory of Generalized Thermo-Elasticity

In this paper, the uniqueness for the linear theory of a new generalized thermo-elastic model of the continuum with the centre symmetry is shown under less assumptions, whose constitutive equations contain deformation, temperature and its rate as well as its gradient, electric field and its gradient. So the phase variation is pemitted when the deformation proceeds as long as the constitutive equations preserve their Original forms.

Global Attractors and Their Dimension Estimates for a Class of Generalized Kirchhoff Equations

In this paper, we studied the long-time properties of solutions of generalized Kirchhoff-type equation with strongly damped terms. Firstly, appropriate assumptions are made for the nonlinear source term g (u) and Kirchhoff stress term M (s) in the equation, and the existence and uniqueness of the solution are proved by using uniform prior estimates of time and Galerkin’s finite element method. Then, abounded absorption set B0k is obtained by prior estimation, and the Rellich-kondrachov’s compact embedding theorem is used to prove that the solution semigroup S (t) generated by the equation has a family of the global attractor Ak in the phase space . Finally, linearize the equation and verify that the semigroups are Frechet diifferentiable on Ek. Then, the upper boundary estimation of the Hausdorff dimension and Fractal dimension of a family of the global attractor Ak was obtained.

Uniqueness and stability of solution for Cauchy problem of degenerate quasilinear parabolic equations

The uniqueness and existence of BV-solutions for Cauchy problem of the form (e)u/(e)t=△A(u)+N∑i=1(e)bi(u)/(e)xi, A'u≥0,u(x,0)=uo are proved.

On the Cauchy Problem of Evolution P-Laplacian Equations with Strongly Non-linear Sources When 1

We study the solvability of the Cauchy problem （1.1）-（1.2） for the largest possible class of initial values,for which （1.1）-（1.2） has a local solution.Moreover,we also study the critical case related to the initial value u0,for 1【p【∞.

SINGULAR PERTURBATION OF THREE-POINT BOUNDARY VALUE PROBLEM FOR THIRD ORDER DIFFERENTIAL EQUATIONS

In this paper, by the theory of differential inequalities, we study the existence and uniqueness of the solution to the three-point boundary value problem for third order differential equations. Furthermore we study the singular perturbation of three-point boundary value problem to third order quasilinear differential equations, construct the higher order asymptotic solution and get the error estimate of asymptotic solution and perturbed solution.

Existence and Uniqueness in Shapefrom Shading

For the image of a smooth surface object fully contained within the field of view and illuminated in an arbitrary direction, this paper discusses the ekistence and uniqueness of the conditions for solving a shape-from-shading problem under the conditions that the Fourier series expansion of the image intensity contains only zero and first order terms in a polar coordinate system. Three theorems are established, one for the ekistence and two for the uniqueness of z-axis symmetric shape from shading.