In this paper we continue the study, which was initiated in (Ben-Artzi et al. in Math. Model. Numer. Anal. 35(2):313–303, 2001; Fishelov et al. in Lecture Notes in Computer Science, vol. 2667, pp. 809–817, 2003; Ben-Artzi et al. in J. Comput. Phys. 205(2):640–664, 2005 and SIAM J. Numer. Anal. 44(5):1997–2024, 2006) of the numerical resolution of the pure streamfunction formulation of the time-...

in this paper‎, ‎we prove a multiplicity result for some biharmonic elliptic equation of kirchhoff type and involving nonlinearities with critical exponential growth at infinity‎. ‎using some variational arguments and exploiting the symmetries of the problem‎, ‎we establish a multiplicity result giving two nontrivial solutions‎.

Barycentric coordinates are an established mathematical tool in computer graphics and geometry processing, providing a convenient way of interpolating scalar or vector data from the boundary of a planar domain to its interior. Many different recipes for barycentric coordinates exist, some offering the convenience of a closedform expression, some providing other desirable properties at the expen...

A new model to describe fractal growth is discussed which includes effects due to long-range coupling between displacements u. The model is based on the biharmonic equation ∇u = 0 in two-dimensional isotropic defect-free media as follows from the Kuramoto-Sivashinsky equation for pattern formation -or, alternatively, from the theory of elasticity. As a difference with Laplacian and Poisson grow...

This paper concerns discontinuous finite element approximations of a fourth-order bi-wave equation arising as a simplified Ginzburg-Landautype model for d-wave superconductors in the absence of an applied magnetic field. In the first half of the paper, we construct a variant of the Morley finite element method, which was originally developed for approximating the fourthorder biharmonic equation...