We consider the inhomogeneous biharmonic nonlinear Schrödinger equation iut+?2u+?|x|?b|u|?u=0,where ?=±1 and ?, b>0. In subctritical case, we improve global well-posedness result obtained in Guzmán Pastor (2020) for dimensions N=5,6,7 Sobolev space H2(RN). The fundamental tools to establish our results are standard Strichartz estimates related linear problem Hardy-Littlewood inequality. Results...

The solvability conditions for a class of boundary value problems nonlocal biharmonic equation in the unit ball with Neumann on are studied. nonlocality is generated by some orthogonal matrix. presence and uniqueness solution to proposed condition examined, an integral representation Dirichlet problem terms Green's function obtained. First, auxiliary statements established: given, this written,...

In this paper, we consider a biharmonic equation with respect to the Dirichlet problem on domain of locally finite graph. Using variation method, prove that has two distinct solutions under certain conditions.

Abstract. We consider multigrid algorithms for the biharmonic problem discretized by conforming 1 finite elements. Most finite elements for the biharmonic equation are nonnested in the sense that the coarse finite element space is not a subspace of the space of similar elements defined on a refined mesh. To define multigrid methods, certain intergrid transfer operators have to be constructed. W...

In a radar imaging problem using broad-band, low-frequency waves, we encounter the problem of solving Poisson's equation over a very large rectangular grid, typically ve thousand times thousand pixels. In addition, no information about boundary values is available. In order to select suitable solutions we solve the Poisson equation under the side condition that some criterion function, usually ...

We explore an application of the Physics-Informed Neural Networks (PINNs) in conjunction with Airy stress functions and Fourier series to find optimal solutions a few reference biharmonic problems elasticity elastic plate theory. Biharmonic relations are fourth-order partial differential equations (PDEs) that challenging solve using classical numerical methods have not been addressed PINNs. Our...