Asymptotic Analysis - Volume 35, issue 2

Authors: Mizoguchi, Noriko

Article Type: Research Article

Abstract: Let p>1 and Ω be a smoothly bounded domain in RN not necessarily convex. This paper is concerned with a Cauchy–Dirichlet problem \def\theequation{(P)}\begin{equation}\left\{\begin{array}{l@{\quad}l}u_{t}=\Delta u+u^{p}&\mbox{in }\varOmega \times (0,\infty),\\[3pt]u(x,t)=0&\mbox{on}\ \curpartial \varOmega \times (0,\infty),\\[3pt]u(x,0)=\phi(x)\geq 0&\mbox{in }\varOmega.\end{array}\right.\end{equation} We show that when u blows up at t=T, it holds |u(t)|∞ ≤C(T−t)−1/(p−1)  in (0,T) with some C>0 under some condition on the Cauchy problem for (P).

Citation: Asymptotic Analysis, vol. 35, no. 2, pp. 91-112, 2003

Authors: Ricciardi, Tonia

Article Type: Research Article

Abstract: We define an abstract nonlinear elliptic system, admitting a variational structure, and including the vortex equations for some Maxwell–Chern–Simons gauge theories as special cases. We analyze the asymptotic behavior of its solutions, and we provide a general simplified framework for the asymptotics previously derived in those special cases. As a byproduct of our abstract formulation, we also find some new qualitative properties of solutions.

Keywords: nonlinear elliptic system, Chern–Simons vortex theory

Citation: Asymptotic Analysis, vol. 35, no. 2, pp. 113-126, 2003

Authors: Guillopé, Colette | Mneimné, Ali | Talhouk, Raafat

Article Type: Research Article

Abstract: In this paper, we study the behaviour, in terms of compressibility, of steady flows of weakly compressible viscoelastic fluids having a differential constitutive law. The models considered here are Jeffreys' and Maxwell's. In both cases, we establish the existence of an asymptotic expansion in the neighbourhood of the steady incompressible fluid flow, with respect to the vanishing isothermal compressibility coefficient.

Keywords: viscoelastic fluids, weak compressibility, convergence, asymptotic behaviour

Citation: Asymptotic Analysis, vol. 35, no. 2, pp. 127-150, 2003

Authors: Apreutesei, N.C. | Volpert, V.A.

Article Type: Research Article

Abstract: The paper is devoted to an elliptic perturbation of a parabolic problem. The solution v of the heat equation with a nonlinear boundary condition is compared with the solution vε of an elliptic regularization. An asymptotic expansion of vε is constructed and the order of accuracy for the difference vε −v is obtained. The boundary function method by Vishik and Lyusternik is used.

Keywords: elliptic regularization, singular perturbations, maximal monotone operator

Citation: Asymptotic Analysis, vol. 35, no. 2, pp. 151-164, 2003

Authors: Junk, Michael | Yong, Wen‐An

Article Type: Research Article

Abstract: In this article, we rigorously investigate the diffusive limit of a velocity‐discrete Boltzmann equation which is used in the lattice Boltzmann method (LBM) to construct approximate solutions of the incompressible Navier–Stokes equation. Our results apply to LBM collision operators with multiple collision frequencies (generalized lattice Boltzmann) which include the widely used BGK operators.

Keywords: lattice Boltzmann method, Navier–Stokes equation, multiple collision frequencies, diffusive scaling, stability, incompressible limit

Citation: Asymptotic Analysis, vol. 35, no. 2, pp. 165-185, 2003