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Asymptotic Analysis - Volume 136, issue 1

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Price: EUR 420.00
ISSN 0921-7134 (P)
ISSN 1875-8576 (E)

Impact Factor 2024: 1.1

The journal Asymptotic Analysis fulfills a twofold function. It aims at publishing original mathematical results in the asymptotic theory of problems affected by the presence of small or large parameters on the one hand, and at giving specific indications of their possible applications to different fields of natural sciences on the other hand. 

Asymptotic Analysis thus provides mathematicians with a concentrated source of newly acquired information which they may need in the analysis of asymptotic problems.

Homogenization of distributive optimal control problem governed by Stokes system in an oscillating domain

Authors: Garg, Swati | Sardar, Bidhan Chandra

Article Type: Research Article

Abstract: The present article deals with the homogenization of a distributive optimal control problem (OCP) subjected to the more generalized stationary Stokes equation involving unidirectional oscillating coefficients posed in a two-dimensional oscillating domain. The cost functional considered is of the Dirichlet type involving a unidirectional oscillating coefficient matrix. We characterize the optimal control and study the homogenization of this OCP with the aid of the unfolding operator. Due to the presence of oscillating matrices both in the governing Stokes equations and the cost functional, one obtains the limit OCP involving a perturbed tensor in the convergence analysis.

Keywords: Homogenization, optimal control, oscillating boundary, unfolding operator, Stokes equations

DOI: 10.3233/ASY-231867

Citation: Asymptotic Analysis, vol. 136, no. 1, pp. 1-26, 2024

Price: EUR 27.50

On the distribution of Born transmission eigenvalues in the complex plane

Authors: Hovsepyan, Narek

Article Type: Research Article

Abstract: We analyze an approximate interior transmission eigenvalue problem in R d for d = 2 or d = 3 , motivated by the transmission problem of a transformation optics-based cloaking scheme and obtained by replacing the refractive index with its first order approximation, which is an unbounded function. Using the radial symmetry we show the existence of (infinitely many) complex transmission eigenvalues and prove their discreteness. Moreover, it is shown that there exists a horizontal strip in the complex plane around the real axis, that does not contain any … Show more

Keywords: Born approximation, transmission eigenvalues, eigenvalue-free regions, inverse scattering, spherically stratified medium

DOI: 10.3233/ASY-231868

Citation: Asymptotic Analysis, vol. 136, no. 1, pp. 27-60, 2024

Price: EUR 27.50

A Jacobi spectral method for calculating fractional derivative based on mollification regularization

Authors: Zhang, Wen | Wu, Changxing | Ruan, Zhousheng | Qiu, Shufang

Article Type: Research Article

Abstract: In this article, we construct a Jacobi spectral collocation scheme to approximate the Caputo fractional derivative based on Jacobi–Gauss quadrature. The convergence analysis is provided in anisotropic Jacobi-weighted Sobolev spaces. Furthermore, the convergence rate is presented for solving Caputo fractional derivative with noisy data by invoking the mollification regularization method. Lastly, numerical examples illustrate the effectiveness and stability of the proposed method.

Keywords: Fractional derivative, Jacobi collocation, mollification, Gaussian quadrature

DOI: 10.3233/ASY-231869

Citation: Asymptotic Analysis, vol. 136, no. 1, pp. 61-77, 2024

Price: EUR 27.50
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