Asymptotic Analysis - Volume 1, issue 4

Authors: Schochet, Steven

Article Type: Research Article

Abstract: Solutions of Whitham's traffic-flow equations are shown to exist globally in time for small values of the response-time parameter, provided that parameter vanishes more rapidly than the cube of the diffusion parameter. In the hyperbolic-hyperbolic singular limit that occurs as the response-time vanishes, the solution converges to the entropy weak solution of the simplified equations.

DOI: 10.3233/ASY-1988-1401

Citation: Asymptotic Analysis, vol. 1, no. 4, pp. 263-282, 1988

Authors: Damlamian, Alain | Hager, William W. | Rostamian, Rouben

Article Type: Research Article

Abstract: We consider a spongy material with tiny holes filled with gas. A formula for the homogenized displacements is derived. It is shown that the solution to the original problem converges weakly in H1 to the solution of the homogenized problem as the diameter of the gas bubbles tends to zero.

DOI: 10.3233/ASY-1988-1402

Citation: Asymptotic Analysis, vol. 1, no. 4, pp. 283-302, 1988

Authors: Jurkat, W.B. | Zwiesler, H.J.

Article Type: Research Article

Abstract: In this paper we address the problem of determining all the meromorphic differential equations that are meromorphically equivalent to a given equation; and we also discuss how one can effectively check whether two given equations are equivalent. In the case of equations of block size 1, which is a generalization of the case of distinct eigenvalues, we provide solutions to these problems which involve only algebraic processes. This allows a detailed description of the structure of the involved transformations. Our discussion is based on the concept of direct transformations which we define and study thoroughly.

DOI: 10.3233/ASY-1988-1403

Citation: Asymptotic Analysis, vol. 1, no. 4, pp. 303-316, 1988

Authors: Gingold, H.

Article Type: Research Article

Abstract: An invariant matrix asymptotic formula for the approximation of solutions of second-order linear ordinary differential equations y″=φ(x)y is proposed and elaborated upon. This is utilized to develop scalar versions of asymptotic formulas for two linearly independent solutions and for their derivatives. This formula is shown to be valid in a half neighbourhood of a point x0 . The validity holds whether x0 is an ordinary (regular) point for the ODE, whether x0 is a singular regular point for the ODE, if some exceptional case is avoided, whether x0 is a singular irregular point for the ODE, and …whether or not x0 is finite. The matrix version of our formulas is shown to be valid also at a turning point. The Liouville-Green approximation is extracted as a particular case of our formula. Examples are given. The formula has additional “globality” properties. Examples are given where the ODE is considered on an infinite interval (0, ∞) and its coefficient φ(x) is singular at x = 0 as well as at x = ∞. A uniformly valid approximation on the entire infinite interval is then provided. Show more

DOI: 10.3233/ASY-1988-1404

Citation: Asymptotic Analysis, vol. 1, no. 4, pp. 317-350, 1988

Article Type: Other

Citation: Asymptotic Analysis, vol. 1, no. 4, pp. 351-351, 1988