Finite time extinction by nonlinear damping for Schrodinger equation

2010/07/01 by Carles, Rémi, Gallo, Clément · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1007.0077

Abstract

We consider the Schrodinger equation on a compact manifold, in the presence of a nonlinear damping term, which is homogeneous and sublinear. For initial data in the energy space, we construct a weak solution, defined for all positive time, which is shown to be unique. In the one-dimensional case, we show that it becomes zero in finite time. In the two and three-dimensional cases, we prove the same result under the assumption of extra regularity on the initial datum.

Cited by

• Cauchy problem for a Schrödinger-type equation related to the Riemann zeta function

Related

• On nonlinear Schrodinger type equations with nonlinear damping
• Existence and nonexistence of global solutions for time-dependent damped NLS equations
• Energy decay for the time dependent damped wave equation
• Finite speed of disturbance for the nonlinear Schrödinger equation
• Sharp polynomial decay for polynomially singular damping on the torus