Asymptotic Analysis - Volume 67, issue 3-4

Authors: Zhan, Mei-Qin

Article Type: Research Article

Abstract: The selective decay phenomena has been observed by physicists for many dynamic flows such as Navier–Stokes flows, barotropic geophysical flows, and magnetohydrodynamic (MHD) flows in either actual physical experiments or numerical simulations. Rigorous mathematical works have been carried out for both Navier–Stokes and barotropic geophysical flows. It is the goal of this paper to verify the selective decay principle mathematically for the 2D magnetohydrodynamic (MHD) flows.

Keywords: selective decay principle, 2D magnetohydrodynamic, vorticity-flux, exponential decay, MHD

DOI: 10.3233/ASY-2009-0972

Citation: Asymptotic Analysis, vol. 67, no. 3-4, pp. 125-146, 2010

Authors: Bourgeat, Alain | Marušić-Paloka, Eduard | Piatnitski, Andrey

Article Type: Research Article

Abstract: We derive a macroscopic model for an underground nuclear waste repository consisting of long storage cells linked by a possibly damaged drifts. As the first result we find a simple first-order approximation. Secondly, we compute a corrector using a matched expansion around the drift. We prove an appropriate convergence result.

Keywords: upscaling, homogenization, convection–diffusion equation

DOI: 10.3233/ASY-2009-0975

Citation: Asymptotic Analysis, vol. 67, no. 3-4, pp. 147-165, 2010

Authors: Gadyl'shin, Rustem R. | Il'in, Arlen M.

Article Type: Research Article

Abstract: The Neumann problem in two-dimensional domain with a narrow slit is studied. The width of the slit is a small parameter 0<ε�1. The complete asymptotic expansion with respect to ε for the eigenvalue of the perturbed problem converging to a simple eigenvalue of the limiting problem is constructed by means of the method of the matching asymptotic expansions. It is shown that the regular perturbation theory can formally be applied in a natural way up to terms of order ε2 . However, the result obtained in that way is false. The correct result can be obtained only by means of …inner asymptotic expansion. We also show that the eigenvalue of the perturbed problem can be both more and less than the eigenvalue of the limiting problem subject to the position and geometry of the slit. Show more

Keywords: singular perturbation, asymptotics, eigenvalues, Neumann problem

DOI: 10.3233/ASY-2009-0976

Citation: Asymptotic Analysis, vol. 67, no. 3-4, pp. 167-189, 2010

Authors: Agarwal, Ravi P. | O'Regan, Donal | Wong, Patricia J.Y.

Article Type: Research Article

Abstract: We consider the system of Hill's equations u″i (t)+ai (t)ui (t)=Fi (t, u1 (t), u2 (t), …, un (t)), 1≤i≤n, where ai and Fi are periodic in t, and the non-linearities Fi (t, x1 , x2 , …, xn ) can be singular at xj =0 where j∈{1, 2, …, n}. Criteria are offered for the existence of periodic constant-sign solutions, i.e., θi ui (t)≥0 for each 1≤i≤n, where θi ∈{1, −1} is fixed. The main tool used is Schauder's fixed point theorem. We also include examples to illustrate the usefulness of the results obtained.

Keywords: constant-sign solutions, system of Hill's equations, singular equations

DOI: 10.3233/ASY-2010-0977

Citation: Asymptotic Analysis, vol. 67, no. 3-4, pp. 191-216, 2010

Authors: Dostanić, Milutin R.

Article Type: Research Article

Abstract: We determine the norm of a class of integral operators induced by the reproducing kernel of Bergman spaces in upper half plane.

Keywords: norm of integral operators, Bergman projection, Berezin transform

DOI: 10.3233/ASY-2010-0979

Citation: Asymptotic Analysis, vol. 67, no. 3-4, pp. 217-228, 2010

Authors: Barles, Guy | Laurençot, Philippe | Stinner, Christian

Article Type: Research Article

Abstract: Convergence to a single steady state is shown for non-negative and radially symmetric solutions to a diffusive Hamilton–Jacobi equation with homogeneous Dirichlet boundary conditions, the diffusion being the p-Laplacian operator, p≥2, and the source term a power of the norm of the gradient of u. As a first step, the radially symmetric and non-increasing stationary solutions are characterized.

Keywords: convergence to steady state, degenerate parabolic equation, viscosity solutions, gradient source term

DOI: 10.3233/ASY-2010-0981

Citation: Asymptotic Analysis, vol. 67, no. 3-4, pp. 229-250, 2010

Article Type: Other

Citation: Asymptotic Analysis, vol. 67, no. 3-4, pp. 251-252, 2010