Asymptotic Analysis - Volume 6, issue 3

Authors: Guillemin, V. | Uribe, A.

Article Type: Research Article

Abstract: We give a new proof of Landau's theorem on the existence of magnetic oscillations in crystals at low temperatures. Our proof is based on the semi-classical trace formula of Paul and Uribe (1991).

DOI: 10.3233/ASY-1993-6301

Citation: Asymptotic Analysis, vol. 6, no. 3, pp. 205-217, 1993

Authors: Budd, C.J. | Peletier, L.A.

Article Type: Research Article

Abstract: We study radially symmetric solutions of the equation Δu+up =0 in annular domains {a<|x|<1} in R3 . In particular we are interested in the behaviour of solutions when the power p tends to the critical Sobolev exponent 5 in R3 and simultaneously, the inner radius shrinks to zero. When p$\searrow$ 5, two forms of behaviour are observed, depending on whether (p−5)2 «a or a«(p−5)2 .

DOI: 10.3233/ASY-1993-6302

Citation: Asymptotic Analysis, vol. 6, no. 3, pp. 219-239, 1993

Authors: Guès, Olivier

Article Type: Research Article

Abstract: We prove existence and stability of high-frequency oscillating solutions for multidimensional quasilinear hyperbolic systems, justifying the asymptotic developments of Choquet-Bruhat (1969). We are concerned with solutions depending on a (small) parameter ε, which admit a development of the form uε (x)=u0 (x)+εu1 (x,ϕ(x)/ε)+…+εM−1 uM−1 (x,ϕ(x)/ε)+O(εM ),(ε→0), where u0 is a given solution of the system, profiles uj (x,θ) are (smooth) 2π-periodic with respect to the fast variable θ∈R, and the integer M is of the order of n/2, n being time-space dimension. We also show that, an arbitrary T>0 being given, one can built such oscillating solutions that remain …regular on the interval of time [0,T] (for every ε>0 enough small). These results are obtained by mean of more general approximation theorems, adapted to the justification of such asymptotic developments. Show more

DOI: 10.3233/ASY-1993-6303

Citation: Asymptotic Analysis, vol. 6, no. 3, pp. 241-269, 1993

Authors: Figari, R. | Teta, A.

Article Type: Research Article

Abstract: We analyze a boundary value problem of mixed type with data prescribed on the union of m spheres of small (order m−1 ) radius. We establish the connection to a particular class of zero-range perturbations of the Laplacian and exploit it for the asymptotic (m→∞) analysis of the solution. It is shown that in the limit problem the “density of scattering length” enters as an effective potential.

DOI: 10.3233/ASY-1993-6304

Citation: Asymptotic Analysis, vol. 6, no. 3, pp. 271-284, 1993

Authors: Rakotoson, Jean Michel

Article Type: Research Article

Abstract: We introduce a new type of sets for problems with L1 -data associated with the standard Leray-Lions operator. The solutions cannot be found in the usual Sobolev spaces.

DOI: 10.3233/ASY-1993-6305

Citation: Asymptotic Analysis, vol. 6, no. 3, pp. 285-293, 1993