Asymptotic Analysis - Volume 34, issue 3-4

Authors: Orsina, Luigi

Article Type: Research Article

Citation: Asymptotic Analysis, vol. 34, no. 3-4, pp. 187-198, 2003

Authors: Ito, Hiroshi T. | Tamura, Hideo

Article Type: Research Article

Abstract: According to the Aharonov–Bohm effect, magnetic potentials have a direct significance to the motion of particles in quantum mechanics. We study this quantum effect through the scattering by several point‐like magnetic fields at large separation in two dimensions. We derive the asymptotic formula for scattering amplitudes as the distances between centers of fields go to infinity. The result heavily depends on the location of centers. A special emphasis is placed on the case of scattering by fields with centers on an even line. The obtained formula depends on fluxes of fields and on ratios of distances between adjacent centers. We …figure the approximate values of differential cross sections to see how the pattern of interferences changes with flux parameters. Show more

Citation: Asymptotic Analysis, vol. 34, no. 3-4, pp. 199-240, 2003

Authors: Murat, François | Sbordone, Carlo

Article Type: Research Article

Citation: Asymptotic Analysis, vol. 34, no. 3-4, pp. 241-259, 2003

Authors: Petrini, Milena

Article Type: Research Article

Abstract: We study an initial values problem related to a viscoelasticity model in a periodic medium, with oscillating data at t=0, looking for the homogenization limit of the associated energy density. This limit is determined in a specific case in which there is a constant proportionality between the elastic coefficient and the one in the viscosity part, where it follows an exponential decay in time of the energy density.

Citation: Asymptotic Analysis, vol. 34, no. 3-4, pp. 261-273, 2003

Authors: Colin, Mathieu

Article Type: Research Article

Abstract: In this article, we study the nonlinear plasma wave equation \[-\varepsilon^{2}\dfrac{\curpartial^{2}u_{\varepsilon}}{\curpartial t^{2}}+2\mathrm{i}\dfrac{\curpartial u_{\varepsilon}}{\curpartial t}+\Delta u_{\varepsilon}=\big(\dfrac{1}{\sqrt{1+|u_{\varepsilon}|^{2}}}-1\big)u_{\varepsilon}+\dfrac{\Delta(\sqrt{1+|u_{\varepsilon}|^{2}})}{\sqrt{1+|u_{\varepsilon}|^{2}}}u_{\varepsilon}\] with initial data $u_{\varepsilon}(\cdot,0)=u_{0}^{\varepsilon}(\cdot)\in H^{8}(\mathbb{R}^{2}),\ \curpartial_{t}u_{\varepsilon}(\cdot,0)=u_{1}^{\varepsilon}(\cdot)\in H^{7}(\mathbb{R}^{2})$ . We show that the Cauchy problem is locally well‐posed on an interval [0,T] where the time T is independent of ε if u1 ε is small enough. Then, we demonstrate the strong convergence of uε towards the solution u of a nonlinear relativistic Schrödinger equation as ε goes to 0.

Citation: Asymptotic Analysis, vol. 34, no. 3-4, pp. 275-309, 2003

Authors: Bourgeat, A. | Mikelić, A. | Piatnitski, A.

Article Type: Research Article

Abstract: We consider the linearized equations of slightly compressible single fluid flow through a highly heterogeneous random porous medium, consisting of two types of material. Due to the high heterogeneity of the two materials the ratio of their permeability coefficients is of order ε2 , where ε is the characteristic scale of heterogeneities. Supposing that the matrix blocks set of the porous medium consists of random stationary inclusions, and assuming positive definiteness of the effective permeability tensor associated to the corresponding Neumann problem for the random fractures system, we obtain the homogenized problem for a random version of the double porosity …model used in geohydrology. It includes as a particular case the periodic setting, already studied by homogenization theory methods (see, for example, [1,7]). The homogenized problem is obtained by using the stochastic two scale convergence in the mean, and by means of convergence results specially adapted to our a priori estimates and to the random geometry, which do not require extension of solutions to the matrix part. Show more

Citation: Asymptotic Analysis, vol. 34, no. 3-4, pp. 311-332, 2003

Authors: Chang, Ya‐Ling | Guo, Jong‐Shenq | Kohsaka, Yoshihito

Article Type: Research Article

Citation: Asymptotic Analysis, vol. 34, no. 3-4, pp. 333-358, 2003

Article Type: Other

Citation: Asymptotic Analysis, vol. 34, no. 3-4, pp. 359-360, 2003