The theory of infinite tube magnetization reversal, formulated by Lee and Chang, has been reconsidered. For this purpose, a standard micromagnetic simulation package OOMMF was used. To account for elongated geometry of ferromagnetic nanotubes grown nowadays, an extension module has been written allowing application of periodic boundary conditions in one dimension. The results of the modelling e...

We prove short time existence and uniqueness of smooth solutions ( in C with k ≥ 2) to the 2-D semi-geostrophic system and semi-geostrophic shallow water system with variable Coriolis parameter f and periodic boundary conditions, under the natural convexity condition on the initial data. The dual space used in analysis of the semi-geostrophic system with constant f does not exist for the variab...

In this paper we present an existence result for a first order impulsive differential inclusion with periodic boundary conditions and impulses at the fixed times under the convex condition of multi-functions.

The no-slip boundary condition at a solid-liquid interface is at the center of our understanding of fluid mechanics. However, this condition is an assumption that cannot be derived from first principles and could, in theory, be violated. In this chapter, we present a review of recent experimental, numerical and theoretical investigations on the subject. The physical picture that emerges is that...

In this paper we address the error growth in time for hyperbolic problems on first order form. The energy method is used to study when an error growth or a fixed error bound is obtained. It is shown that the choice of boundary procedure is a crucial point. Numerical experiments corroborate the theoretical findings. 1. Introduction. Stable approximations of hyperbolic problems on first order for...

Keywords: Dirichlet boundary value problem p-Laplacian Topological degree theory Critical point theory Weak solution a b s t r a c t In this work, by virtue of topological degree theory and critical point theory, we are mainly concerned with the existence of weak solutions for a Dirichlet boundary value problem with the p-Laplacian operator.

In this paper, we consider the long time behavior of solutions for two-dimensional generalized Benjamin-Bona-Mahony equations with periodic boundary conditions. By the method of orthogonal decomposition, we show that the existence of asymptotic attractor from the precision of approximate inertial manifolds. Moreover, the dimensions estimate of the asymptotic attractor is obtained.

singular perturbation problems have been studied by many mathematicians. since the approximate solutions of these problems are as the sum of internal solution (boundary layer area) and external ones, the formation or non-formation of boundary layers should be specified. this paper, investigates this issue for a singular perturbation problem including a first order differential equation with gen...

We extend the trace formula recently proven for general one-dimensional Schrödinger operators which obtains the potential V (x) from a function ξ(x,λ) by deriving trace relations computing moments of ξ(x,λ)dλ in terms of polynomials in the derivatives of V at x. We describe the relation of those polynomials to KdV invariants. We also discuss trace formulae for analogs of ξ associated with bound...