Asymptotic Analysis - Volume 5, issue 1

Authors: Fife, Paul C. | Hastings, Stuart P. | Lu, Chunqing

Article Type: Research Article

Abstract: An asymptotic analysis is given for the system of nonlinear second order ordinary differential equations modeling the propagation of a flame with chemical reactions typical of reversible chain branching kinetics. The basic small parameter is the inverse of the activation energy of first forward reaction, but 2 other parameters enter prominently into the analysis. A thorough formal analysis is given for this problem, and the asymptotics is justified, in its essential features, through a rigorous analysis.

DOI: 10.3233/ASY-1991-5101

Citation: Asymptotic Analysis, vol. 5, no. 1, pp. 1-26, 1991

Authors: Balser, W. | Braaksma, B.L.J. | Ramis, J.-P. | Sibuya, Y.

Article Type: Research Article

Abstract: If f is a formal power series solution of a linear meromorphic differential equation, then it is shown that f=f1 +…+fq , were fj is hj -summable; here h1 ,…hq are slopes of the associated Newton polygon. The multisummability properties of fundamental solutions of linear homogeneous meromorphic differential equations are studied.

DOI: 10.3233/ASY-1991-5102

Citation: Asymptotic Analysis, vol. 5, no. 1, pp. 27-45, 1991

Authors: Braides, Andrea

Article Type: Research Article

Abstract: In a previous paper (Braides et al., 1990) it has been proven, under very mild almost periodicity conditions, that we have weak convergence in H1,p (Ω) of the solutions uε of boundary problems in an open set Ω related to the quasi-linear monotone operator −div(a(x/ε,Duε )), to a function u, which solves an analogous problem related to a homogenized operator −div(b(Du)). In general we do not have strong convergence of Duε , to Du in (Lp (Ω))n , even in the linear periodic case. It is possible however (Theorems 2.1 and 4.2) to express Duε in …terms of Du, up to a rest converging strongly to 0 in (Lp (Ω))n , applying correctors built up exploiting only the geometric properties of a. In the last section, we use the correctors result to obtain a homogenization theorem for quasi-linear equations with natural growth terms. Show more

DOI: 10.3233/ASY-1991-5103

Citation: Asymptotic Analysis, vol. 5, no. 1, pp. 47-74, 1991

Authors: Boccardo, L. | Del Vecchio, T.

Article Type: Research Article

Abstract: This paper deals with the G-convergence of some quasi-linear elliptic equations, when the lower order term has sub-quadratic growth with respect to the gradient.

DOI: 10.3233/ASY-1991-5104

Citation: Asymptotic Analysis, vol. 5, no. 1, pp. 75-90, 1991