Asymptotic behavior of the solutions of a system of Schödinger-Poisson equations on a bounded domain in \(\mathbb R ^3 \)
type: Item
instance of: scholarly article
title: Asymptotic behavior of the solutions of a system of Schödinger-Poisson equations on a bounded domain in \(\mathbb R ^3 \)
zbMATH Open document ID: 1218.35043
author: Amna Dabaa
published in: Annales Mathématiques Blaise Pascal
publication date: 2010-07-27T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/116349
review text: The weakly damped driven Schrödinger-Poisson system \[ \partial_t u+\gamma u+i\Delta u+iu\varphi=f , \qquad \pm\Delta\varphi=|u|^2 \] for \((t,x)\in (0,\infty)\times\Omega\) is considered in a bounded domain \(\Omega\) of \(\mathbb R^3\), supplemented with homogeneous Dirichlet boundary conditions for \(u\) and \(\varphi\) and an initial condition \(u_0\in H^1_0(\Omega)\). Assuming that the driving force \(f\) belongs to \(L^2(\Omega)\) and the damping parameter \(\gamma\) is positive, the existence of a compact attractor with finite Hausdorff dimension in \(H_0^1(\Omega)\) is shown.
reviewed by: Philippe Laurençot
Mathematics Subject Classification ID: 35B41
Mathematics Subject Classification ID: 35Q55
zbMATH DE Number: 5761667
zbMATH Keywords: absorbing set
zbMATH Keywords: weak damping
zbMATH Keywords: homogeneous Dirichlet boundary conditions
zbMATH Keywords: driving force
MaRDI profile type: Publication
OpenAlex ID: W2090488186
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DOI: 10.5802/AMBP.283
description: scientific article; zbMATH DE number 5761667