Searching for just a few words should be enough to get started. If you need to make more complex queries, use the tips below to guide you.
Purchase individual online access for 1 year to this journal.
Price: EUR 420.00Impact 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.
Authors: D’Abbicco, Marcello | Ebert, Marcelo Rempel
Article Type: Research Article
Abstract: In this paper we study the asymptotic profile (as t → ∞ ) of the solution to the Cauchy problem for the linear plate equation u t t + Δ 2 u − λ ( t ) Δ u + u t = 0 when λ = λ ( t ) is a decreasing function, assuming initial data in the energy space and verifying a moment condition. For sufficiently small data, we find the critical exponent …for global solutions to the corresponding problem with power nonlinearity u t t + Δ 2 u − λ ( t ) Δ u + u t = | u | p . In order to do that, we assume small data in the energy space and, possibly, in L 1 . In this latter case, we also determinate the asymptotic profile of the solution to the semilinear problem for supercritical power nonlinearities. Show more
Keywords: Asymptotic profile, diffusion phenomena, critical exponents, plate equation
DOI: 10.3233/ASY-201624
Citation: Asymptotic Analysis, vol. 123, no. 1-2, pp. 1-40, 2021
Authors: Deugoué, G. | Tachim Medjo, T.
Article Type: Research Article
Abstract: In this article, we derive a large deviation principle for a 2D Allen–Cahn–Navier–Stokes model under random influences. The model consists of the Navier–Stokes equations for the velocity, coupled with an Allen–Cahn equation for the order (phase) parameter. The proof relies on the weak convergence method that was introduced in (Ann. Inst. Henri Poincaré Probab. Stat. 47 (2011 ) 725–747) and based on a variational representation on infinite-dimensional Brownian motion.
Keywords: Allen–Cahn, Navier–Stokes, strong solutions, Gaussian noise, large deviations
DOI: 10.3233/ASY-201625
Citation: Asymptotic Analysis, vol. 123, no. 1-2, pp. 41-78, 2021
Authors: Esposito, Luca | Roy, Prosenjit | Sk, Firoj
Article Type: Research Article
Abstract: We analyze the asymptotic behavior of the eigenvalues of nonlinear elliptic problems under Dirichlet boundary conditions and mixed (Dirichlet, Neumann) boundary conditions on domains becoming unbounded. We make intensive use of Picone identity to overcome nonlinearity complications. Altogether the use of Picone identity makes the proof easier with respect to the known proof in the linear case. Surprisingly the asymptotic behavior under mixed boundary conditions critically differs from the case of pure Dirichlet boundary conditions for some class of problems.
Keywords: Eigenvalues problems, ℓ goes to plus infinity, dimension reduction
DOI: 10.3233/ASY-201626
Citation: Asymptotic Analysis, vol. 123, no. 1-2, pp. 79-94, 2021
Authors: Xu, Yao | Niu, Weisheng
Article Type: Research Article
Abstract: This paper concentrates on the quantitative homogenization of higher-order elliptic systems with almost-periodic coefficients in bounded Lipschitz domains. For almost-periodic coefficients in the sense of H. Weyl, we establish uniform local L 2 estimates for the approximate correctors. Under an additional assumption (1.8 ) on the frequencies of the coefficients, we derive the existence of true correctors as well as the O ( ε ) convergence rate in H m − 1 . As a byproduct, the large-scale Hölder estimate and a Liouville theorem are obtained …for higher-order elliptic systems with almost-periodic coefficients in the sense of Besicovitch. Since (1.8 ) is not well-defined for equivalence classes of almost-periodic functions in the sense of H. Weyl or Besicovitch, we provide another condition yielding the O ( ε ) convergence rate under perturbations of the coefficients. Show more
Keywords: Almost periodic homogenization, higher-order elliptic systems, quantitative estimates
DOI: 10.3233/ASY-201627
Citation: Asymptotic Analysis, vol. 123, no. 1-2, pp. 95-137, 2021
Authors: Bahrouni, Anouar | Ho, Ky
Article Type: Research Article
Abstract: In this paper, we give some properties of the new fractional Sobolev spaces with variable exponents and apply them to study a class of eigenvalue problems involving the fractional p ( · ) -Laplace operator. We obtain sequences of eigenvalues going asymptotically to infinity and we also establish sufficient conditions to get zero value for the principal eigenvalue, which is a striking difference between the variable exponent case and the constant exponent case. As an application, we obtain several existence and nonexistence results for the eigenvalue problem according to the asymptotic growth of the nonlinearity and the range …of the spectral parameter. Show more
Keywords: Fractional Sobolev spaces, variable exponents, eigenvalue problems, variational methods
DOI: 10.3233/ASY-201628
Citation: Asymptotic Analysis, vol. 123, no. 1-2, pp. 139-156, 2021
Authors: Melo, Wilberclay G. | Rocha, Natã F. | Zingano, Paulo R.
Article Type: Research Article
Abstract: This work guarantees the existence of a positive instant t = T and a unique solution ( u , w ) ∈ [ C ( [ 0 , T ] ; H a , σ s ( R 2 ) ) ] 3 (with a > 0 , σ > 1 , s > 0 and s ≠ 1 ) for the micropolar equations. Furthermore, we consider the global existence in time of this solution …in order to prove the following decay rates: lim t → ∞ t s 2 ‖ ( u , w ) ( t ) ‖ H ˙ a , σ s ( R 2 ) 2 = lim t → ∞ t s + 1 2 ‖ w ( t ) ‖ H ˙ a , σ s ( R 2 ) 2 = lim t → ∞ ‖ ( u , w ) ( t ) ‖ H a , σ λ ( R 2 ) = 0 , ∀ λ ⩽ s . These limits are established by applying the estimate ‖ F − 1 ( e T | · | ( u ˆ , w ˆ ) ( t ) ) ‖ H s ( R 2 ) ⩽ [ 1 + 2 M 2 ] 1 2 , ∀ t ⩾ T , where T relies only on s , μ , ν and M (the inequality above is also demonstrated in this paper). Here M is a bound for ‖ ( u , w ) ( t ) ‖ H s ( R 2 ) (for all t ⩾ 0 ) which results from the limits lim t → ∞ t s 2 ‖ ( u , w ) ( t ) ‖ H ˙ s ( R 2 ) = lim t → ∞ ‖ ( u , w ) ( t ) ‖ L 2 ( R 2 ) = 0 . Show more
Keywords: Micropolar equations, decay rates, Sobolev–Gevrey spaces
DOI: 10.3233/ASY-201630
Citation: Asymptotic Analysis, vol. 123, no. 1-2, pp. 157-179, 2021
Authors: Wang, Danhua | Liu, Wenjun
Article Type: Research Article
Abstract: In this paper, we consider the Cauchy problem related to the standard linear solid model with Gurtin–Pipkin thermal law in the whole space. Under some assumptions on the relaxation function g , we establish the well-posedness result by using semigroup theory. Besides, by using the energy method in the Fourier space, we prove the decay estimate result under the non-critical case. Our result indicates that the decay property is of the regularity-loss type, which is in line with the decay property of Cattaneo system.
Keywords: Well-posedness, the standard linear solid model, Gurtin–Pipkin thermal law, decay estimate
DOI: 10.3233/ASY-201631
Citation: Asymptotic Analysis, vol. 123, no. 1-2, pp. 181-201, 2021
IOS Press, Inc.
6751 Tepper Drive
Clifton, VA 20124
USA
Tel: +1 703 830 6300
Fax: +1 703 830 2300
sales@iospress.com
For editorial issues, like the status of your submitted paper or proposals, write to editorial@iospress.nl
IOS Press
Nieuwe Hemweg 6B
1013 BG Amsterdam
The Netherlands
Tel: +31 20 688 3355
Fax: +31 20 687 0091
info@iospress.nl
For editorial issues, permissions, book requests, submissions and proceedings, contact the Amsterdam office info@iospress.nl
Inspirees International (China Office)
Ciyunsi Beili 207(CapitaLand), Bld 1, 7-901
100025, Beijing
China
Free service line: 400 661 8717
Fax: +86 10 8446 7947
china@iospress.cn
For editorial issues, like the status of your submitted paper or proposals, write to editorial@iospress.nl
如果您在出版方面需要帮助或有任何建, 件至: editorial@iospress.nl