Finite Time Extinction by Nonlinear Damping for the Schrödinger Equation

DOI10.1080/03605302.2010.531074zbMath1228.35040arXiv1007.0077OpenAlexW2962767311MaRDI QIDQ3104539

Rémi Carles, Clément Gallo

Publication date: 14 December 2011

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1007.0077

zbMATH Keywords

Coulomb frictionSchrödinger equationNash inequalitysublinear friction term

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) NLS equations (nonlinear Schrödinger equations) (35Q55)

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Cites Work

• Unnamed Item
• Unnamed Item
• A note on the dynamics of an oscillator in the presence of strong friction.
• On universality of blow up profile for \(L^2\) critical nonlinear Schrödinger equation
• Asymptotics for some nonlinear damped wave equation: finite time convergence versus exponential decay results
• Self-Focusing in the Damped Nonlinear Schrödinger Equation
• Global Well-Posedness for Cubic NLS with Nonlinear Damping
• Continuity of Solutions of Parabolic and Elliptic Equations
• Stabilization of Schrödinger equation in exterior domains