Asymptotic Analysis - Volume 111, issue 3-4

Authors: Badanin, Andrey | Korotyaev, Evgeny L.

Article Type: Research Article

Abstract: We consider fourth order ordinary differential operator with compactly supported coefficients on the line. We define resonances as zeros of the Fredholm determinant which is analytic on a four sheeted Riemann surface. We determine estimates of the number of resonances in complex discs at large radius. We consider resonances of an Euler–Bernoulli operator on the real line with the positive coefficients which are constants outside some finite interval. We show that the Euler–Bernoulli operator has no eigenvalues and resonances iff the positive coefficients are constants on the whole axis.

Keywords: Fourth order operators, resonances, scattering, trace formula

DOI: 10.3233/ASY-181489

Citation: Asymptotic Analysis, vol. 111, no. 3-4, pp. 137-177, 2019

Authors: Qin, Yuming | Su, Keqin

Article Type: Research Article

Abstract: This paper is concerned with the dynamics of 2D Navier–Stokes–Voight equations which govern an incompressible fluid flow. By virtue of energy estimates and compact embedding technique, we establish the existence of finite fractal dimensional global attractor for the 2D Navier–Stokes–Voight equations with a distributed delay.

Keywords: Navier–Stokes–Voight equations, distributed delay, global attractor, fractal dimension

DOI: 10.3233/ASY-181492

Citation: Asymptotic Analysis, vol. 111, no. 3-4, pp. 179-199, 2019

Authors: Peng, Shuiran | Zhu, Hongyi

Article Type: Research Article

Abstract: Our aim in this paper is to study a modified higher-order (in space) phase field crystal model taking anisotropy into account. In particular, we deduce a priori estimates to prove well-posedness results and the dissipativity of the semigroup.

Keywords: Modified phase field crystal equation, higher-order models, anisotropy, a priori estimates, dissipative semigroup

DOI: 10.3233/ASY-181494

Citation: Asymptotic Analysis, vol. 111, no. 3-4, pp. 201-215, 2019

Authors: Dalla Riva, Matteo | Musolino, Paolo | Pukhtaievych, Roman

Article Type: Research Article

Abstract: We study the asymptotic behavior of the effective thermal conductivity of a periodic two-phase dilute composite obtained by introducing into an infinite homogeneous matrix a periodic set of inclusions of a different material, each of them of size proportional to a positive parameter ϵ . We assume that the normal component of the heat flux is continuous at the two-phase interface, while we impose that the temperature field displays a jump proportional to the normal heat flux. For ϵ small, we prove that the effective conductivity can be represented as a convergent power series in ϵ and we …determine the coefficients in terms of the solutions of explicit systems of integral equations. Show more

Keywords: Effective conductivity, periodic dilute composite, singularly perturbed domain, asymptotic expansion, non-ideal contact condition

DOI: 10.3233/ASY-181495

Citation: Asymptotic Analysis, vol. 111, no. 3-4, pp. 217-250, 2019