A method for evaluation of scattering from rough surfaces which is similar to the Kirchhoff approximation is considered. However, it is based on a local parabolic approximation of the surface irregularities rather than a tangent plane approximation and two iterations of the surface field integral equation. The method, first proposed by Belobrov and Fuks [Izv. VUZ Radiofiz. 29, 1083-1089 (1986);...

In this paper we obtain the constitutive equation for the second Piola-Kirchhoff stress tensor according to the linearized finite theory of elasticity for hyperelastic constrained materials. We show that in such a theory the three stress tensors (Cauchy stress tensor, first and second Piola-Kirchhoff stress tensor) differ by terms that are first order in the strain, while in classical linear th...

In this paper, we study Kirchhoff type problems on a bounded domain. We consider the cases that the nonlinearity is superlinear near zero but asymptotically 4-linear at infinity, and the nonlinearity is asymptotically linear near zero but 4-superlinear at infinity. By computing the relevant critical groups, we obtain nontrivial solutions via Morse theory.

In this article, by using critical point theory, we show the existence of infinitely many weak solutions for a fourth-order Kirchhoff type elliptic problems with Hardy potential.

Article history: Received 26 November 2016 Accepted after revision 3 April 2017 Available online 18 April 2017 Presented by the Editorial Board The aim of this note is to present the almost global well-posedness result for the Cauchy problem for the Kirchhoff equation with large data in Gevrey spaces. We also briefly discuss the corresponding results in bounded and in exterior domains. © 2017 A...

Abstract The objects of consideration are thin linearly thermoelastic Kirchhoff-Love-type circular cylindrical shells having a periodically microheterogeneous structure in circumferential and axial directions ( biperiodic ). aim this contribution is to formulate discuss two new averaged mathematical models for the analysis selected dynamic thermoelasticity problems under consideration: non-asym...

We consider the curve straightening flow of inextensible, open, planar curves generated by the Kirchhoff bending energy. It can be considered as a model for the motion of elastic, inextensible rods in a high friction regime. We derive governing equations, namely a semilinear fourth order parabolic equation for the indicatrix and a second order elliptic equation for the Lagrange multiplier. We p...