Asymptotic Analysis - Volume 86, issue 3-4

Authors: Nazarov, S.A. | Specovius-Neugebauer, M. | Steigemann, M.

Article Type: Research Article

Abstract: A crack approaching a material interface between two elastic materials may stop or may advance by either penetrating the interface or deflecting into the interface (cf. N.Y. He and J.W. Hutchinson, Int. J. Solids Struct. 25 (1989), 1053–1067). Mathematical models for crack path prediction are based on the asymptotic behavior near the crack tip. In this work, an idea to compute the asymptotic expansion of the displacement field for structures composed of two dissimilar elastic anisotropic materials is shown, if the crack impinges the material interface. In contrast to the well-known case of isotropic materials, logarithmic terms can appear in …the asymptotic decomposition of the displacement field in anisotropic composites. Based on this results, the energy release rate is calculated for different scenarios of crack propagation in composite structures. Show more

Keywords: energy principle, anisotropic composite materials, stress intensity factors, crack propagation

DOI: 10.3233/ASY-131187

Citation: Asymptotic Analysis, vol. 86, no. 3-4, pp. 123-153, 2014

Authors: Said-Houari, Belkacem

Article Type: Research Article

Abstract: In this paper, we study the decay rates of solutions for the generalized Benjamin–Bona–Mahony equation in multi-dimensional space. For initial data in some L1 -weighted spaces, we prove faster decay rates of the solutions. More precisely, using the Fourier transform and the energy method, we show the global existence and the convergence rates of the solutions under the smallness assumption on the initial data and we give better decay rates of the solutions. This result improves early works in J. Differential Equations 158(2) (1999), 314–340 and Nonlinear Anal. 75(7) (2012), 3385–3392.

Keywords: decay of solutions, Benjamin–Bona–Mahony equation, global existence, energy method

DOI: 10.3233/ASY-131191

Citation: Asymptotic Analysis, vol. 86, no. 3-4, pp. 155-164, 2014

Authors: Briane, Marc | Pater, Laurent

Article Type: Research Article

Abstract: In this paper we study the magneto-resistance, i.e. the second-order term of the resistivity perturbed by a low magnetic field, of a three-dimensional composite material. Extending the two-dimensional periodic framework of [Mathematical Models and Methods in Applied Sciences 20(7) (2010), 1161–1177], it is proved through a H-convergence approach that the dissipation energy induced by the effective magneto-resistance is greater or equal to the average of the dissipation energy induced by the magneto-resistance in each phase of the composite. This inequality validates for a composite material the Kohler law which is known for a homogeneous conductor. The case of equality is …shown to be very sensitive to the magnetic field orientation. We illustrate the result with layered and columnar periodic structures. Show more

Keywords: hall effect, homogenization, magneto-resistance, magneto-transport

DOI: 10.3233/ASY-131192

Citation: Asymptotic Analysis, vol. 86, no. 3-4, pp. 165-197, 2014

Authors: Li, Tatsien | Rao, Bopeng

Article Type: Research Article

Abstract: In this paper, the asymptotic null controllability and various kinds of asymptotic synchronization, as some sorts of weakened controllability and synchronization, are introduced and studied for a coupled system of wave equations with Dirichlet boundary controls. Equivalent properties of observability are established and several examples of explanation are also given.

Keywords: asymptotic null controllability, D-observability, asymptotic synchronization, asymptotic null controllability and synchronization by groups, asymptotic synchronization by groups, CD-observability

DOI: 10.3233/ASY-131193

Citation: Asymptotic Analysis, vol. 86, no. 3-4, pp. 199-226, 2014

Authors: Fatori, L.H. | Muñoz Rivera, J.E. | Nunes Monteiro, R.

Article Type: Research Article

Abstract: We consider the thermoelastic beam system when the oscillations are defined by the Timoshenko's model and the heat conduction is given by Green and Naghdi theories. Our main result is that the corresponding semigroup is exponentially stable if and only if the wave speeds associated to the hyperbolic part of the system are equal. In the case of lack of exponential stability we show that the solution decays polynomially and we prove that the rate of decay is optimal.

Keywords: Timoshenko system, decay rates, optimality of polynomial stability

DOI: 10.3233/ASY-131196

Citation: Asymptotic Analysis, vol. 86, no. 3-4, pp. 227-247, 2014

Article Type: Other

Citation: Asymptotic Analysis, vol. 86, no. 3-4, pp. 249-249, 2014