Asymptotic Analysis - Volume 50, issue 3-4

Authors: Capdeboscq, Yves | Vogelius, Michael S.

Article Type: Research Article

Abstract: The main result of this paper establishes optimal pointwise bounds for the polarization tensors that appear in representation formulae for the voltage perturbations caused by low volume fraction inhomogeneities. Furthermore it is demonstrated how these pointwise bounds may be used to derive a particularly simple version of the representation formulae in the case of thin inhomogeneities.

Citation: Asymptotic Analysis, vol. 50, no. 3-4, pp. 175-204, 2006

Authors: Immink, G.K.

Article Type: Research Article

Abstract: We prove the existence of Gevrey type solutions for locally analytic, nonlinear difference equations possessing a formal solution that belongs to some (generalized) Gevrey class of divergent power series in z−1/p . We consider different types of domains: domains bounded by a curve with limiting directions −π/2 and π/2 (mod  π), and domains bounded by curves with the same limiting direction, viz. π/2 (mod  π), containing an unbounded part of the imaginary axis.

Citation: Asymptotic Analysis, vol. 50, no. 3-4, pp. 205-237, 2006

Authors: Matsuyama, Tokio | Reissig, Michael

Article Type: Research Article

Abstract: The goal of the paper is to derive Strichartz estimates for solutions to wave equations with time-dependent coefficients belonging to Cr , 2≤r≤2n+1, and generating an anisotropic speed of propagation. A stabilization condition for the coefficients is introduced. This condition allows to show the Log-effect in Lp –Lq estimates and explains in this way the loss of decay.

Keywords: Strichartz estimates, loss of decay, WKB-solutions, Fourier multipliers, stabilization, low regularity of coefficients

Citation: Asymptotic Analysis, vol. 50, no. 3-4, pp. 239-268, 2006

Authors: Chepyzhov, Vladimir V. | Mainini, Edoardo | Pata, Vittorino

Article Type: Research Article

Abstract: We establish some decay properties of the semigroup generated by a linear integro-differential equation in a Hilbert space, which is an abstract version of the equation ut (t)−βΔu(t)−∫0 ∞ k(s)Δu(t−s) ds=0 describing hereditary heat conduction.

Keywords: hereditary heat conduction, memory kernels, contraction semigroups, stability, exponential stability

Citation: Asymptotic Analysis, vol. 50, no. 3-4, pp. 269-291, 2006

Authors: Nodet, Maëlle

Article Type: Research Article

Abstract: We consider the linear Primitive Equations of the ocean in the three-dimensional space, with horizontal periodic and vertical Dirichlet boundary conditions. Thanks to Fourier transforms we are able to calculate explicitly the pressure term. We then state existence, unicity and regularity results for the linear time-depending Primitive Equations, with low-regularity right-hand side.

Citation: Asymptotic Analysis, vol. 50, no. 3-4, pp. 293-324, 2006

Authors: Baillet, Séverine | Henrot, Antoine | Takahashi, Takéo

Article Type: Research Article

Abstract: In this paper, we study the asymptotic behavior of the solution of a semilinear problem and of a Stokes problem, with periodic data, when the size of the domain increases. In particular, we prove exponential convergence to the solution of the corresponding problem with periodic boundary conditions.

Citation: Asymptotic Analysis, vol. 50, no. 3-4, pp. 325-337, 2006

Article Type: Other

Citation: Asymptotic Analysis, vol. 50, no. 3-4, pp. 339-340, 2006

Article Type: Other

Citation: Asymptotic Analysis, vol. 50, no. 3-4, pp. 341-348, 2006