Asymptotic Analysis - Volume 37, issue 2

Authors: Kato, Jun | Ozawa, Tohru

Article Type: Research Article

Abstract: In this article, the behavior of solutions to the free wave equation with homogeneous Cauchy data are considered. In particular, the propagation of singularities are observed explicitly. Such Cauchy data are of special interest in view of applications to self‐similar solutions to nonlinear wave equations.

Citation: Asymptotic Analysis, vol. 37, no. 2, pp. 93-107, 2004

Authors: D'Aprile, Teresa

Article Type: Research Article

Abstract: In this paper we are concerned with the problem of finding solutions for the following nonlinear field equation −ħ2 Δv+V(x)v−ħp Δp v+W′ (v)=0, where v : $\mathbb{R} $ N →$\mathbb{R} $ N+1 , N≥3, p>N, ħ>0, the potential V is positive and W is an appropriate singular function. Assuming that V has a mountain pass geometry, determined by the existence of two strict local minima, then for small values of the parameter ħ we are able to find a solution which concentrates at the related mountain pass point of V in the semiclassical limit (i.e., as ħ→0+ …). The proof of our results uses a variational approach and the solutions are captured as critical points for the associated energy functional. Show more

Citation: Asymptotic Analysis, vol. 37, no. 2, pp. 109-141, 2004

Authors: Ben Abdallah, Naoufel | Chaker, Hédia

Article Type: Research Article

Abstract: In a previous paper (Math. Methods Models Appl. Sci. 11 (2001), 1253–1272), the high field limit for degenerate semiconductors is analyzed by the authors. The scope of the present paper is the extention of this analysis to boundary value problems. The initial layer, modeled by a homogeneous Boltzmann equation with a frozen electric field provides an initial condition for the high field solution. The boundary layers, analyzed by means of Milne problems, are shown to provide boundary condition for the limit equation on that part of the boundary corresponding to an inflowing flux, while they connect the fluid and kinetic …data on the outgoing part of the boundary. Under some monotonicity assumptions on the high field solution (which are satisfied at least for low densities), the asymptotic behaviour of the Milne problem is exhibited. These results are used to provide an error estimate for the high field asymptotics. Show more

Keywords: kinetic equations, maximum principle, convergence rate, boundary layer, initial layer

Citation: Asymptotic Analysis, vol. 37, no. 2, pp. 143-174, 2004

Authors: Vodev, Georgi

Article Type: Research Article

Citation: Asymptotic Analysis, vol. 37, no. 2, pp. 175-187, 2004