Asymptotic Analysis - Volume 57, issue 1-2

Authors: Reissig, Michael | Wirth, Jens

Article Type: Research Article

Abstract: In this note we develop tools and techniques for the treatment of anisotropic thermo-elasticity in two space dimensions. We use a diagonalisation technique to obtain properties of the characteristic roots of the full symbol of the system in order to prove Lp –Lq decay rates for its solutions.

Keywords: thermo-elasticity, a-priori estimates, anisotropic media

DOI: 10.3233/ASY-2008-0863

Citation: Asymptotic Analysis, vol. 57, no. 1-2, pp. 1-27, 2008

Authors: Wirth, Jens

Article Type: Research Article

Abstract: This note deals with concrete applications of the general treatment of anisotropic thermo-elasticity developed in the first part, Asympt. Anal. 57 (2008). We give dispersive decay rates for solutions to the type-1 system of thermo-elasticity for certain types of anisotropic media.

Keywords: thermo-elasticity, a-priori estimates, anisotropic media

DOI: 10.3233/ASY-2008-0883

Citation: Asymptotic Analysis, vol. 57, no. 1-2, pp. 29-40, 2008

Authors: Jung, Chang-Yeol

Article Type: Research Article

Abstract: In this article, we discuss reaction-diffusion problems which produce ordinary boundary layers and elliptic corner layers. Using the classical polynomial Q1 -finite elements spaces enriched with the so-called boundary layer elements which absorb the singularities due to the boundary and corner layers we are able to attain high numerical accuracies. We essentially obtain ε-uniform approximation errors in a weighted energy norm with significant simplifications in the numerical implementations; here we do not use mesh refinements.

Keywords: boundary layers, finite elements, singularly perturbed problem, reaction-diffusion, enriched subspaces

DOI: 10.3233/ASY-2008-0865

Citation: Asymptotic Analysis, vol. 57, no. 1-2, pp. 41-69, 2008

Authors: Hamchi, Ilhem

Article Type: Research Article

Abstract: In this paper, we consider a second-order hyperbolic equations with variable coefficients and linear lower-order term. We use a new main multiplier and a suitable nonlinear version of a compactness uniqueness argument (Acta. Math. Sin. – Engl. Ser. 20(6) (2004), 1057–1072) to obtain the exponential stabilization of this system where no condition of smallness is needed.

Keywords: Riemann geometry method, uniqueness continuation result

DOI: 10.3233/ASY-2008-0867

Citation: Asymptotic Analysis, vol. 57, no. 1-2, pp. 71-82, 2008

Authors: Squassina, Marco

Article Type: Research Article

Abstract: We investigate the long term behavior for a class of competition–diffusion systems of Lotka–Volterra type for two competing species in the case of low regularity assumptions on the data. Due to the coupling that we consider the system cannot be reduced to a single equation yielding uniform estimates with respect to the inter-specific competition rate parameter. Moreover, in the particular but meaningful case of initial data with disjoint support and Dirichlet boundary data which are time-independent, we prove that as the competition rate goes to infinity the solution converges, along with suitable sequences, to a spatially segregated state satisfying some …variational inequalities. Show more

Keywords: competition–diffusion systems, Lotka–Volterra model, spatial segregation, population dynamics, asymptotic behaviour, stationary solution, dissipative systems

DOI: 10.3233/ASY-2008-0868

Citation: Asymptotic Analysis, vol. 57, no. 1-2, pp. 83-103, 2008

Authors: Mihailovici, Monika | Schweizer, Ben

Article Type: Research Article

Abstract: We study a pore scale model for the reactive layer of a fuel cell and derive effective equations. The cathode catalytic layer has a complex micro-structure to facilitate the transport of ion-gases and electrons. The reaction takes place at the surface of catalyst particles that are small compared to the pore space dimensions. The surface reaction law incorporates an exponential nonlinearity. The mathematical treatment is based on maximum principles and introduces a measure valued variant of compensated compactness.

Keywords: homogenization, surface reaction, effective equation, fuel cell

DOI: 10.3233/ASY-2008-0876

Citation: Asymptotic Analysis, vol. 57, no. 1-2, pp. 105-123, 2008