In this paper, we consider the well-posedness of inhomogeneous nonlinear biharmonic Schrödinger equation with spatial inhomogeneity coefficient K(x) behaves like |x|−b for 0<b<min⁡{N2,4}. We show local in whole Hs-subcritical case, 0<s≤2. The difficulties problem come from singularity and lack differentiability term. To resolve this, derive bilinear Strichartz's type estimates equations Besov s...

The solution of the equations governing the two-dimensional slow viscous fluid flow is analysed using a novel technique based on a Laplacian decomposition instead of the more traditional approaches based on the biharmonic streamfunction formulation or the velocity-pressure formulation. This results in the need to solve three Laplace equations for the pressure and two auxiliary harmonic function...

Let T be a tree rooted at e endowed with a nearest-neighbor transition probability that yields a recurrent random walk. We show that there exists a function K biharmonic off e whose Laplacian has potential theoretic importance and, in addition, has the following property: Any function f on T which is biharmonic outside a finite set has a representation, unique up to addition of a harmonic funct...

SUMMARY Applying a finite difference approximation to a biharmonic equation results in a very ill-conditioned system of equations. This paper examines the conjugate gradient method ' used in con junction with the generalized and approximate polynomial preconditionings for solving such linear systems. An approximate polynomial preconditioning is introduced, and is shown to be more efficient than...

We investigate proper biharmonic hypersurfaces with at most three distinct principal curvatures in space forms. We obtain the full classification of proper biharmonic hypersurfaces in 4-dimensional space forms.

In the present paper we survey the most recent classification results for proper biharmonic submanifolds in unit Euclidean spheres. We also obtain some new results concerning geometric properties of proper biharmonic constant mean curvature submanifolds in spheres.