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...

In this study, a high accuracy numerical method based on the spectral theory of compact operator for biharmonic eigenvalue equations on a spherical domain is developed. By employing the orthogonal spherical polynomials approximation and the spectral theory of compact operator, the error estimates of approximate eigenvalues and eigenfunctions are provided. By adopting orthogonal spherical base f...

The diffusive and directed transport of particles in a two-dimensional periodic potential subjected to frictional and time-periodic forces is analyzed in detail. The model represents diffusion of atoms adsorbed on metal surfaces under an applied ac electric field (surface electromigration) in the low-temperature limit. The second dimension and the potential energy coupling are shown to play an ...

In this work, we compare different mesh moving techniques for monolithically-coupled fluid-structure interactions in arbitrary Lagrangian–Eulerian coordinates. The mesh movement is realized by solving an additional partial differential equation of harmonic, linear-elastic, or biharmonic type. We examine an implementation of time discretization that is designed with finite differences. Spatial d...

A hypersurface is said to be totally biharmonic if all its geodesics are curves in the ambient space. We prove that a into space form an isoparametric hypersurface, which allows us give full classification of hypersurfaces these spaces. Moreover, restricting ourselves 3-dimensional case, we show surfaces Bianchi–Cartan–Vranceanu spaces and their classification. In particular, that, leaving asid...

We construct new explicit proper biharmonic functions on the 3-dimensional Thurston geometries Sol, Nil, S̃L2(R), H 2 × R and

In this paper we give an enclosure for the solution of the biharmonic problem and also for its gradient and Laplacian in the L2-norm, respectively.