Asymptotic Analysis - Volume 42, issue 1-2

Authors: Kamotski, V. | Lebeau, G.

Article Type: Research Article

Citation: Asymptotic Analysis, vol. 42, no. 1-2, pp. 1-27, 2005

Authors: Carrillo, José A. | Fellner, Klemens

Article Type: Research Article

Abstract: Uniform convergence rates of diffusion dominated equations towards their asymptotic profiles are quantified via entropy methods for bounded integrable non‐negative initial data with finite entropy. Convergence rates are sharp since they coincide with the purely diffusive ones. The approach is applied to both convection– and absorption–diffusion equations. Finally, Wasserstein metrics are used to control the expansion of the support for the convection–diffusion case.

Keywords: convection–diffusion, absorption–diffusion, entropy methods, large time behaviour, convergence rate

Citation: Asymptotic Analysis, vol. 42, no. 1-2, pp. 29-54, 2005

Authors: Sakamoto, Kunimochi

Article Type: Research Article

Abstract: For a propagator–controller type system of reaction–diffusion equations on an N‐dimensional ball, it is shown that there exists a family of radially symmetric stationary transition layer solutions when the propagator diffuses slowly compared with the controller. A spectral analysis is also carried out for the linearization around the layered solutions, which reveals that these layer‐solutions are unstable. More importantly, it is found that for activator(propagator)–inhibitor(controller) systems there exist infinitely many static bifurcation points from the radially symmetric solutions as the diffusion rate of the activator goes to zero. This confirms the validity of a conjecture raised in Proc. Roy. Soc. …Edinburgh Sect. A 128 (1998), 359–401, in the special situation where the domain is a ball. Show more

Keywords: reaction–diffusion system, radial symmetry, internal layer, interface equation, bifurcation

Citation: Asymptotic Analysis, vol. 42, no. 1-2, pp. 55-104, 2005

Authors: Guillarmou, Colin

Article Type: Research Article

Abstract: As a consequence of a result of Cardoso–Vodev, we show that the resolvent of the Laplacian on asymptotically hyperbolic manifolds is analytic in an exponential neighbourhood of the critical line $\{\Re(\lambda )=\frac{n}{2}\}$ . The case of non‐trapping metrics with constant curvature near infinity is also considered: there is a strip $\{\Re(\lambda )>\frac{n}{2}-\varepsilon\}$ with a finite number of resonances.

Citation: Asymptotic Analysis, vol. 42, no. 1-2, pp. 105-121, 2005

Authors: Amar, M. | Dall'Aglio, A. | Paronetto, F.

Article Type: Research Article

Abstract: We study the homogenization of the equation \[R(\varepsilon ^{-1}x)\frac{ \curpartial u_{\varepsilon }}{\curpartial t}-\Delta u_{\varepsilon }=f,\] where R is a periodic function which may vanish or change sign, with appropriate initial/final conditions. The main tool is a compactness result for sequences of functions which have bounded norms in the spaces associated to the problems.

Citation: Asymptotic Analysis, vol. 42, no. 1-2, pp. 123-132, 2005

Authors: Sili, Ali

Article Type: Research Article

Abstract: We study the homogenization of an elastic medium periodically reinforced by thin anisotropic elastic fibers, the radius of the fibers being of the order of the size ε of the period, while 1/ε2 is the ratio between the coefficients of the tensor inside the fibers with those of the tensor outside them. In this case, the sequence uε of the displacements is not apriori bounded in (L2 (Ω))3 . We prove that the homogenized problem is a strongly coupled nonlocal problem which involves variables due to the anisotropy of the fibers.

Keywords: homogenization, anisotropic, elasticity, fibers

Citation: Asymptotic Analysis, vol. 42, no. 1-2, pp. 133-171, 2005