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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 numerical solutions of time-delayed reaction diffusion equations with non-monotone reaction term

Yuan-Ming Wang (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

This paper is concerned with the asymptotic behavior of the finite difference solutions of a class of nonlinear reaction diffusion equations with time delay. By introducing a pair of coupled upper and lower solutions, an existence result of the solution is given and an attractor of the solution is obtained without monotonicity assumptions on the nonlinear reaction function. This attractor is a sector between two coupled quasi-solutions of the corresponding “steady-state” problem, which are obtained...

Asymptotic behavior of the numerical solutions of time-delayed reaction diffusion equations with non-monotone reaction term

Yuan-Ming Wang (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper is concerned with the asymptotic behavior of the finite difference solutions of a class of nonlinear reaction diffusion equations with time delay. By introducing a pair of coupled upper and lower solutions, an existence result of the solution is given and an attractor of the solution is obtained without monotonicity assumptions on the nonlinear reaction function. This attractor is a sector between two coupled quasi-solutions of the corresponding “steady-state" problem, which are...

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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