In this paper, we first establish regularity of the heat flow of biharmonic maps into the unit sphere S ⊂ R under a smallness condition of renormalized total energy. For the class of such solutions to the heat flow of biharmonic maps, we prove the properties of uniqueness, convexity of hessian energy, and unique limit at t = ∞. We establish both regularity and uniqueness for Serrin’s (p, q)-sol...

A mixed formulation with two main variables, based on the Ciarlet-Raviart technique, with 0 C continuity shape functions is employed for the solution of some types of biharmonic equations in 1-D. The continuous and discrete Babuška-Brezzi inf-sup conditions are established. The formulation is numerically tested for both the hand pextensions. The model problems involve the standard biharmonic eq...

This paper is concerned with weak solution of a mixed boundary value problem for the biharmonic equation in the plane. Using Green’s formula, the problem is converted into a system of Fredholm integral equations for the unknown data on different part of the boundary. Existence and uniqueness of the solutions of the system of boundary integral equations are established in appropriate Sobolev spa...

In this paper, we investigate the existence of infinitely many solutions for a class of biharmonic equations where the nonlinearity involves a combination of superlinear and asymptotically linear terms. The solutions are obtained from a variant version of Fountain Theorem.

Biharmonic equation is one of the most existing operator in many areas, especially in fluid and solid mechanics, but difficult to solve due to the fourth order derivatives in the differential equation. In this paper we deal with the use of the local particular solution method to solve the two-dimensional biharmonic equation in a bounded region. The technique is based on decoupling the biharmoni...

Iterative methods to achieve a suitable linearization as well as a decrease of the order and dimension of nonlinear partial differential equations of the eighth order into the biharmonic and Poisson-type differential equations with their simultaneous linearization are proposed in this work. Validity and reliability of the obtained results are discussed using computer programs developed by the a...

A. In this paper, by applying the first variation formula of f -bi-energy given in [OND], we study f -biharmonic maps between doubly warped product manifolds M ×(μ,λ) N. Under imposing existence condition concerning proper f -biharmonic maps, we derive f -biharmonicity’s characteristic equations for the inclusion maps: iy0 : (M, g) → (M ×(μ,λ) N, ḡ), ix0 : (N, h) → (M ×(μ,λ) N, ḡ) and th...