Asymptotic Analysis - Volume 9, issue 1

Authors: Herrero, M.A. | Lacey, A.A. | Velazquez, J.J.L.

Article Type: Research Article

Abstract: Consider the problem (1) ut =uxx +δeu ,   if 0<x<1,t>0, (2) u(0,t)=asin ωt,  u(1,t)=0 for t≥0, (3) u(x,0)=u0 (x), where a>0,ω>0, and u0 (x) is a continuous and bounded real function. If we replace the first condition in (2) by u(0,t)=0, it is known that the corresponding Cauchy-Dirichlet problem (P0 ) is characterized by the existence of a critical parameter δF K such that (i) If δ>δF K, every solution of (P0 ) blows up in finite time, and (ii) If δ<δF K there exist global solutions of (P0 ) for some choices of u0 (x). A similar …parameter δc =δc (a,ω) exists for problem (1)-(3) and is such that δc ≤δF K. We obtain here an asymptotic formula for δc (a,ω) when a or ω (or both) are arbitrarily large. Show more

DOI: 10.3233/ASY-1994-9101

Citation: Asymptotic Analysis, vol. 9, no. 1, pp. 1-22, 1994

Authors: Fuchs, Martin

Article Type: Research Article

Abstract: We amsider (local) minimizers u∈H1,p (Ω,RN ) of variational integrals ℱ(u):=∫Ω f(Du)dx with integrand f coming asymptotically close to |Du|p for large values of Du and prove everywhere regularity theorems without imposing any differentiability or convexity conditions on f. Further sections contain applications to certain relaxed problems.

DOI: 10.3233/ASY-1994-9102

Citation: Asymptotic Analysis, vol. 9, no. 1, pp. 23-38, 1994

Authors: Heibig, A.

Article Type: Research Article

Abstract: This paper deals with solutions of a homogenized hyperbolic system of conservation laws. Recently, Weinan E (case of a one-dimensional compressible fluid, cf. [3]) and D. Serre (general case of a one-dimensional system of conservation laws, cf. [11]) derived a system of homogenized equations, by using a multiple scale analysis. Our goal is to prove the existence of solutions for such a system.

DOI: 10.3233/ASY-1994-9103

Citation: Asymptotic Analysis, vol. 9, no. 1, pp. 39-45, 1994

Authors: Miara, B.

Article Type: Research Article

Abstract: The method of asymptotic expansions used by P.G. Ciarlet and his co-workers for justifying the two-dimensional Kirchhoff Love theory of linearly or nonlinearly elastic plates relies in a crucial way on appropriate sea lings of the components of the displacement and appropriate assumptions on the data (Lamé constants and applied forces). We give here a complete justification of these scalings and assumptions on the data in the linearized case.

DOI: 10.3233/ASY-1994-9104

Citation: Asymptotic Analysis, vol. 9, no. 1, pp. 47-60, 1994

Authors: Anzellotti, G. | Baldo, S. | Percivale, D.

Article Type: Research Article

Abstract: We consider families of variational problems Fε over domains Ωε whose extension in one or more directions is small compared to the extension in the other directions, and goes to zero while ε tends to zero. We study then the “variational” convergence of the functionals Fε to a new functional defined on a domain A in a lower dimensional space, where those “dimensions” that were small in Ωε disappear. A general framework is presented in the first part of the paper and an application to the elastic rod and the elastic plate is given in the …second part. Show more

DOI: 10.3233/ASY-1994-9105

Citation: Asymptotic Analysis, vol. 9, no. 1, pp. 61-100, 1994