Asymptotic Analysis - Volume 3, issue 1

Authors: Raikov, G.D.

Article Type: Research Article

Abstract: We consider an ideal linear magnetohydrodynamic model with translational symmetry and investigate the spectral properties of the force operator Ak with a fixed longitudinal wavenumber k. We establish that the essential spectrum of Ak consists of two bounded segments (slow magnetosonic and Alfvén continuum). Next, we show that the isolated eigenvalues of Ak do not accumulate to the tips of the Alfvén continuum. Further, we obtain detailed information about the asymptotics of the eigenvalues of Ak which lie to the right of the essential spectrum and tend to +∞. At last, in the case when the …two segments of the essential spectrum of Ak are disjoint, we find that, generically, the isolated eigenvalues of Ak accumulate to the right tip of the slow magnetosonic continuum, and calculate the first asymptotic term of the corresponding infinite eigenvalue sequence. Show more

DOI: 10.3233/ASY-1990-3101

Citation: Asymptotic Analysis, vol. 3, no. 1, pp. 1-35, 1990

Authors: Frank, L.S.

Article Type: Research Article

DOI: 10.3233/ASY-1990-3102

Citation: Asymptotic Analysis, vol. 3, no. 1, pp. 37-41, 1990

Authors: Gmira, Abdelilah

Article Type: Research Article

Abstract: In this paper we prove that a nontrivial solution of the quasilinear parabolic ut =div(|∇|p−2 ∇u)−uq in RN ×(0,T),u(x,0)=0 for x≠0, p>2 exists if and only if 0<q<p−1+p/N.

DOI: 10.3233/ASY-1990-3103

Citation: Asymptotic Analysis, vol. 3, no. 1, pp. 43-56, 1990

Authors: Qi, Tang

Article Type: Research Article

Abstract: Starting with a three-dimensional Hencky model on an open set ω×]−ε,ε[, we give a mathematical justification of two-dimensional elastoplastic plate models. Following the work of Duvaut, Lions and Temam, we use the variational form of elastoplastic problems as the starting point of discussion and we use the theory of Γ-convergence to examine the limiting behaviour of the problem when ε→0. We conclude that the solutions of three-dimensional plate problems converge to those of two-dimensional plate problems under regularity hypotheses on the boundary conditions. Finally, convergence of the limit analysis energy is also verified.

DOI: 10.3233/ASY-1990-3104

Citation: Asymptotic Analysis, vol. 3, no. 1, pp. 57-76, 1990

Authors: Amirat, Youcef | Hamdache, Kamel | Ziani, Abdelhamid

Article Type: Research Article

Abstract: We consider a 1-D model for incompressible miscible displacements in porous media without any dispersion term. Existence and uniqueness results for nonsmooth data are proved. We study the homogenization of the model. The limit problem is of the same type. The result is obtained thanks to compactness properties of the corresponding characteristic curves.

DOI: 10.3233/ASY-1990-3105

Citation: Asymptotic Analysis, vol. 3, no. 1, pp. 77-89, 1990