This paper is the second in a series of two in which we care about the asymptotics of the three-dimensional displacement field in thin elastic plates as the thickness tends to zero. In Part I we have investigated four types of lateral boundary conditions when the transverse component is clamped. In this Part II we study four other types of lateral conditions when the transverse component is fre...

Wave-equation migration is an accurate and robust alternative to Kirchhoff migration when multipathing and other complex wave phenomena occur, such as in subsalt exploration. In these situations, images obtained by wave-equation migration are often superior to images obtained by Kirchhoff methods. However, 3-D wave-equation prestack imaging is an immature technology compared with Kirchhoff imag...

The resistance distance between any two vertices of G is defined as the network effective resistance between them if each edge of G is replaced by a unit resistor. The Kirchhoff index Kf(G) is the sum of resistance distances between all the pairs of vertices in G. We firstly provided an exact formula for the Kirchhoff index of the hypercubes networks Q n by utilizing spectral graph theory. More...

The Kirchhoff analogy for elastic rods establishes the equivalence between the solutions of the classical spinning top and the stationary solutions of the Kirchhoff model for thin elastic rods with circular cross-sections. In this paper the Kirchhoff analogy is further generalized to show that the classical Kovalevskaya solution for the rigid body problem is formally equivalent to the solution ...

Firstand second-order reflection coefficients are presented for the small slope approximation. The first-order reflection coefficient is identical to the Kirchhoff, or physical optics, result, and the secondorder reflection coefficient reduces to those of perturbation theory and the Kirchhoff approximation in the appropriate limits. Numerical results are obtained for acoustic or TE-polarized el...

In this paper, we studied the long-time properties of solutions generalized Kirchhoff-type equation with strongly damped terms. Firstly, appropriate assumptions are made for nonlinear source term g (u) and Kirchhoff stress term M (s) in equation, existence uniqueness solution proved by using uniform prior estimates time Galerkin’s finite element method. Then, abounded absorption set B0k is obta...

Abstract In this article, we study the following general Kirchhoff type equation: ? M ? R 3 ? ? u <m:mn...

In this paper, a high-order iterative scheme is established in order to get convergent sequence at rate of N, (N ≥ 2) local unique weak solution nonlinear Kirchhoff-type wave equation associated with Robin conditions.

We consider the existence and uniqueness of solution to a fourth-order Kirchhoff type elliptic equation with strong singularity. By using Ekeland’s variational principle in suitable subsets $H_0^2(\Omega )$, we obtain necessary sufficient conditi