TY - JOUR
T1 - Finite Time Extinction for Nonlinear Schrödinger Equation in 1D and 2D
AU - Carles, Rémi
AU - Ozawa, Tohru
N1 - Funding Information:
RC was supported by the French ANR projects SchEq (ANR-12-JS01-0005-01) and BECASIM (ANR-12-MONU-0007-04).
Publisher Copyright:
© 2015, Taylor & Francis Group, LLC.
PY - 2015/1/1
Y1 - 2015/1/1
N2 - We consider a nonlinear Schrödinger equation with power nonlinearity, either on a compact manifold without boundary, or on the whole space in the presence of harmonic confinement, in space dimension one and two. Up to introducing an extra superlinear damping to prevent finite time blow up, we show that the presence of a sublinear damping always leads to finite time extinction of the solution in 1D, and that the same phenomenon is present in the case of small mass initial data in 2D.
AB - We consider a nonlinear Schrödinger equation with power nonlinearity, either on a compact manifold without boundary, or on the whole space in the presence of harmonic confinement, in space dimension one and two. Up to introducing an extra superlinear damping to prevent finite time blow up, we show that the presence of a sublinear damping always leads to finite time extinction of the solution in 1D, and that the same phenomenon is present in the case of small mass initial data in 2D.
KW - Asymptotic behavior
KW - Finite time extinction
KW - Nonlinear Schrödinger equation
KW - Nonlinear damping
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U2 - 10.1080/03605302.2014.967356
DO - 10.1080/03605302.2014.967356
M3 - Article
AN - SCOPUS:84926051828
SN - 0360-5302
VL - 40
SP - 897
EP - 917
JO - Communications in Partial Differential Equations
JF - Communications in Partial Differential Equations
IS - 5
ER -