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Asymmetric heteroclinic double layers

Michelle Schatzman (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Let W be a non-negative function of class C3 from 2 to , which vanishes exactly at two points a and b. Let S1(a, b) be the set of functions of a real variable which tend to a at -∞ and to b at +∞ and whose one dimensional energy E 1 ( v ) = ∫ W ( v ) + | v ' | 2 / 2 x is finite. Assume that there exist two isolated minimizers z+ and z- of the energy E1 over S1(a, b). Under a mild coercivity condition on the potential W and a generic spectral condition on the linearization of the one-dimensional Euler–Lagrange operator at z+ and...

Asymptotic analysis for the Ginzburg-Landau equations

Tristan Rivière (1999)

Bollettino dell'Unione Matematica Italiana

Questo lavoro costituisce un survey sui problemi di limite asintotico per le soluzioni delle equazioni di Ginzburg-Landau in dimensione due. Vengono presentati essenzialmente i risultati di [BBH] e [BR] sulla formazione ed il comportamento asintotico dei vortici in un dominio bidimensionale nel caso fortemente repulsivo (large K limit).

Asymptotic Analysis of a Schrödinger-Poisson System with Quantum Wells and Macroscopic Nonlinearities in Dimension 1

Faraj, A. (2010)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 35Q02, 35Q05, 35Q10, 35B40.We consider the stationary one dimensional Schrödinger-Poisson system on a bounded interval with a background potential describing a quantum well. Using a partition function which forces the particles to remain in the quantum well, the limit h®0 in the nonlinear system leads to a uniquely solved nonlinear problem with concentrated particle density. It allows to conclude about the convergence of the solution.

Asymptotic behavior of a steady flow in a two-dimensional pipe

Piotr Bogusław Mucha (2003)

Studia Mathematica

The paper investigates the asymptotic behavior of a steady flow of an incompressible viscous fluid in a two-dimensional infinite pipe with slip boundary conditions and large flux. The convergence of the solutions to data at infinities is examined. The technique enables computing optimal factors of exponential decay at the outlet and inlet of the pipe which are unsymmetric for nonzero fluxes of the flow. As a corollary, the asymptotic structure of the solutions is obtained. The results show strong...

Asymptotic behavior of solutions to Schrödinger equations near an isolated singularity of the electromagnetic potential

Veronica Felli, Alberto Ferrero, Susanna Terracini (2011)

Journal of the European Mathematical Society

Asymptotics of solutions to Schrödinger equations with singular magnetic and electric potentials is investigated. By using a Almgren type monotonicity formula, separation of variables, and an iterative Brezis–Kato type procedure, we describe the exact behavior near the singularity of solutions to linear and semilinear (critical and subcritical) elliptic equations with an inverse square electric potential and a singular magnetic potential with a homogeneity of order −1.

Asymptotic Behavior of the Solution of the Distribution Diffusion Equation for FENE Dumbbell Polymer Model

I. S. Ciuperca, L. I. Palade (2011)

Mathematical Modelling of Natural Phenomena

This paper deals with the evolution Fokker-Planck-Smoluchowski configurational probability diffusion equation for the FENE dumbbell model in dilute polymer solutions. We prove the exponential convergence in time of the solution of this equation to a corresponding steady-state solution, for arbitrary velocity gradients.

Asymptotic behavior of the solutions to a one-dimensional motion of compressible viscous fluids

Shigenori Yanagi (1995)

Mathematica Bohemica

We study the one-dimensional motion of the viscous gas represented by the system v t - u x = 0 , u t + p ( v ) x = μ ( u x / v ) x + f ∫ 0 x v x ¨ , t , with the initial and the boundary conditions ( v ( x , 0 ) , u ( x , 0 ) ) = ( v 0 ( x ) , u 0 ( x ) ) , u ( 0 , t ) = u ( X , t ) = 0 . We are concerned with the external forces, namely the function f , which do not become small for large time t . The main purpose is to show how the solution to this problem behaves around the stationary one, and the proof is based on an elementary L 2 -energy method.

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