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The journal Asymptotic Analysis fulfills a twofold function. It aims at publishing original mathematical results in the asymptotic theory of problems affected by the presence of small or large parameters on the one hand, and at giving specific indications of their possible applications to different fields of natural sciences on the other hand.
Asymptotic Analysis thus provides mathematicians with a concentrated source of newly acquired information which they may need in the analysis of asymptotic problems.
Authors: Ghomari, Kaoutar | Messirdi, Bekkai | Vũ Ngọc, San
Article Type: Research Article
Abstract: This article reviews the Birkhoff–Gustavson normal form theorem (BGNF) near an equilibrium point of a quantum Hamiltonian. The BGNF process is thereafter used to investigate the spectrum of Schrödinger operators in the 1:1, 1:2 and 1:3 resonances. A computer program is proposed to compute the coefficients of the BGNF up to any order.
Keywords: Birkhoff normal form, harmonic oscillator, Bargmann representation, resonances, Fermi resonance
DOI: 10.3233/ASY-131186
Citation: Asymptotic Analysis, vol. 85, no. 1-2, pp. 1-28, 2013
Authors: Poliakovsky, Arkady
Article Type: Research Article
Abstract: We develop a variational technique for some wide classes of nonlinear evolutions. The novelty here is that we derive the main information directly from the corresponding Euler–Lagrange equations. In particular, we prove that not only the minimizer of the appropriate energy functional but also any critical point must be a solution of the corresponding evolutional system.
Keywords: evolution equations, variational principles
DOI: 10.3233/ASY-131171
Citation: Asymptotic Analysis, vol. 85, no. 1-2, pp. 29-74, 2013
Authors: Wu, Hao | Jiang, Jie
Article Type: Research Article
Abstract: In this paper, we study the Cauchy problem of a time-dependent drift-diffusion-Poisson system for semiconductors. Existence and uniqueness of global weak solutions are proven for the system with a higher-order nonlinear recombination-generation rate R. We also show that the global weak solution will converge to a unique equilibrium as time tends to infinity.
Keywords: drift-diffusion-Poisson system, global weak solution, uniqueness, long-time behavior
DOI: 10.3233/ASY-131176
Citation: Asymptotic Analysis, vol. 85, no. 1-2, pp. 75-105, 2013
Authors: Fila, Marek | Ishige, Kazuhiro | Kawakami, Tatsuki
Article Type: Research Article
Abstract: We consider the following initial value problem for a two-dimensional semilinear elliptic equation with a dynamical boundary condition: −Δu=up , x∈R2 + , t>0, ∂t u+∂ν u=0, x∈∂R2 + , t>0, u(x,0)=φ(x1 )≥0, x=(x1 ,0)∈∂R2 + , where u=u(x,t), ∂t :=∂/∂t, ∂ν :=−∂/∂x2 , R2 + :={(x1 ,x2 ): x1 ∈R,x2 >0} and p>1. We show that small solutions behave asymptotically like suitable multiples of the Poisson kernel. This is an extension of previous results of the authors of this paper to the two-dimensional case.
Keywords: semilinear elliptic equation in a half-plane, dynamical boundary condition, large time behavior
DOI: 10.3233/ASY-131183
Citation: Asymptotic Analysis, vol. 85, no. 1-2, pp. 107-123, 2013
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