The evaluation of sums (matrix-vector products) of the solutions of the three-dimensional biharmonic equation can be accelerated using the fast multipole method, while memory requirements can also be significantly reduced. We develop a complete translation theory for these equations. It is shown that translations of elementary solutions of the biharmonic equation can be achieved by considering ...

In this paper, non-geodesic biharmonic curves in ̃ SL(2, R) space are characterized and the statement that only proper biharmonic curves are helices is proved. Also, the explicit parametric equations of proper biharmonic helices are obtained. AMS subject classifications: 53A40

Biharmonic equations have many applications, especially in fluid and solid mechanics, but difficult to solve due to the fourth order derivatives in the differential equation. In this paper a fast second order accurate algorithm based on a finite difference discretization and a Cartesian grid is developed for two dimensional biharmonic equations on irregular domains with essential boundary condi...

Biharmonic equations have many applications, especially in fluid and solid mechanics, but difficult to solve due to the fourth order derivatives in the differential equation. In this paper a fast second order accurate algorithm based on a finite difference discretization and a Cartesian grid is developed for two dimensional biharmonic equations on irregular domains with essential boundary condi...

Abstract. We give a new proof of regularity of biharmonic maps from four-dimensional domains into spheres, showing first that the biharmonic map system is equivalent to a set of bilinear identities in divergence form. The method of reverse Hölder inequalities is used next to prove continuity of solutions and higher integrability of their second order derivatives. As a byproduct, we also prove t...

The evaluation of sums (matrix–vector products) of the solutions of the three-dimensional biharmonic equation can be accelerated using the fast multipole method, while memory requirements can also be significantly reduced. We develop a complete translation theory for these equations. It is shown that translations of elementary solutions of the biharmonic equation can be achieved by considering ...

The use of the biharmonic operator for deforming a mesh in an arbitrary-Lagrangian-Eulerian simulation is investigated. The biharmonic operator has the advantage that two conditions can be specified on each boundary of the mesh. This allows both the position and the normal mesh spacing along a boundary to be controlled, which is important for two-fluid interfaces and periodic boundaries. At the...

Abstract: This paper deals with the study of the numerical solution of biharmonic equations in one dimension. Biharmonic equations appear frequently in many areas of engineering and physics representing some phenomena. The solution of such problems have been tackled by many authors. In this paper, a numerical method based on the Adomian decomposition method is introduced for the approximate sol...

In this paper, we study the existence of multiple solutions to a class of p-biharmonic elliptic equations, pu – pu + V(x)|u|p–2u = λh1(x)|u|m–2u + h2(x)|u|q–2u, x ∈RN , where 1 0. By variational methods, we obtain the existence of infini...

The behavior of solutions to the biharmonic equation is well-understood in smooth domains. In the past two decades substantial progress has also been made for the polyhedral domains and domains with Lipschitz boundaries. However, very little is known about higher order elliptic equations in the general setting. In this paper we introduce new integral identities that allow to investigate the sol...