Let (M, g) be a four dimensional compact Riemannian manifold without boundary, (N, h) ⊂ R be a compact Riemannian submanifold without boundary. We establish the existence of a global weak solution to the heat flow of extrinsic biharmonic maps from M to N , which is smooth away from finitely many singular times. As a consequence, we prove that if Π4(N) = {0}, then any free homotopy class α ∈ [M,...

In this paper we establish some results of existence infinitely many solutions for an elliptic equation involving the p-biharmonic and p-Laplacian operators coupled with Navier boundary conditions where nonlinearities depend on two real parameters do not satisfy any symmetric condition. The nature approach is variational main tool abstract result Ricceri. novelty in application use a class test...

We consider a single Chua’s circuit and a system of a unidirectionally coupled n-Chua’s circuits driven by a biharmonic signal with two widely different frequencies ω and Ω, where Ω ω. We show experimental evidence for vibrational resonance in the single Chua’s circuit and undamped signal propagation of a low-frequency signal in the system of n-coupled Chua’s circuits where only the first circu...

This paper reports a new spectral collocation method for numerically solving two-dimensional biharmonic boundary-value problems. The construction of the Chebyshev approximations is based on integration rather than conventional differentiation. This use of integration allows: (i) the imposition of the governing equation at the whole set of grid points including the boundary points and (ii) the s...

Abstract. We modify the usual biharmonic model, still frequently used in the engineering community to model linearly elastic plates. In its traditional form, the biharmonic model diverges in general, since it does not incorporate shear effects. Our changes make it convergent for all loads, under a usual assumption on how the loads depend on the thickness. The idea is to add “higher order” terms...

An analytical method to find the flow generated by the basic singularities of Stokes flow in a wedge of arbitrary angle is presented. Specifically, we solve a biharmonic equation for the stream function of the flow generated by a point stresslet singularity and satisfying no-slip boundary conditions on the two walls of the wedge. The method, which is readily adapted to any other singularity typ...

In this article, we prove the existence and uniqueness of solutions for the Dirichlet problem (P ) { ∆(ω(x)|∆u|∆u)− div[ω(x)|∇u|∇u] = f(x)− div(G(x)), in Ω u(x) = 0, in ∂Ω where Ω is a bounded open set of R (N≥2), f∈L (Ω, ω) and G/ω∈[L (Ω, ω)] .

We first obtain Liouville type results for stable entire solutions of the biharmonic equation −∆2u = u−p in R for p > 1 and 3 ≤ N ≤ 12. Then we consider the Navier boundary value problem for the corresponding equation and improve the known results on the regularity of the extremal solution for 3 ≤ N ≤ 12. As a consequence, in the case of p = 2, we show that the extremal solution u∗ is regular w...