Topic
Asymptotology
About: Asymptotology is a research topic. Over the lifetime, 1319 publications have been published within this topic receiving 35831 citations.
Papers published on a yearly basis
Papers
More filters
••
TL;DR: In this article, the majorant function that is used in connection with the comparison technique is usually assumed to be non-increasing in the dependent variable, however, properties of the asymptotic manifold are discussed here under the opposite monotonicity assumption.
Abstract: The asymptotic properties of the solutions of a linear homogeneous system of differential equations determine, under suitable restrictions, the asymptotic properties of a set of solutions of a nonlinear perturbation of this linear equation. The comparison principle is used here to generate an asymptotic manifold of the perturbed equation. The majorant function that is used in connection with the comparison technique is usually assumed to be nondecreasing in the dependent variable. However, properties of the asymptotic manifold are discussed here under the opposite monotonicity assumption, namely, that the majorant function is nonincreasing in the dependent variable. This type of majorant, function arises, for example, in certain gravitation problems. The main result on the structure of asymptotic manifolds which have an asymptotic uniformity is that solutions close to the manifold are either in the manifold or do not exist in the future.
5 citations
••
TL;DR: In this article, a first-order asymptotic representation is developed for low and intermediate-degree p-modes in stars for which the lower boundary of the resonant acoustic cavity is not located close to the star's centre.
Abstract: A first-order asymptotic representation is developed for low- and intermediate-degree p-modes in stars for which the lower boundary of the resonant acoustic cavity is not located close to the star's centre. To this end, afourth-order system of differential equations in the radial parts of the divergence and the radial component of the Lagrangian displacement is adopted. The lower boundary of the resonant acoustic cavity is considered to be a turning point for one of the differential equations. As in a previous asymptotic study of low-degree p-modes with high radial orders, asymptotic expansion procedures applying to self-adjoint second-order differential equations with a large parameter are used by extension of these methods. The main result is that, in contrast with the usual first-order asymptotic theory for low-degree p-modes of high radial orders, the present first-order asymptotic representation leads to small frequency separations D n , f different from zero. The validity of the asymptotic representation is tested for p-modes of the equilibrium sphere with uniform mass density, since the modes of this model are determined by means of exact analytical solutions.
5 citations
••
5 citations
••
5 citations
••
TL;DR: In this article, asymptotic expansions of solutions of the first initial boundary value problem for strong Schrodinger systems near a conical point of the boundary of a domain are considered.
Abstract: We consider asymptotic expansions of solutions of the first initial boundary-value problem for strong Schrodinger systems near a conical point of the boundary of a domain
5 citations