EXISTENCE AND NONEXISTENCE OF GLOBAL SOLUTIONS FOR TIME-DEPENDENT DAMPED NLS EQUATIONS

Makram Hamouda; Mohamed Majdoub

doi:10.3934/cpaa.2023100

EXISTENCE AND NONEXISTENCE OF GLOBAL SOLUTIONS FOR TIME-DEPENDENT DAMPED NLS EQUATIONS

Makram Hamouda^*
, Mohamed Majdoub

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We investigate the Cauchy problem for the nonlinear Schrödinger equation with a time-dependent linear damping term. Under non standard assumptions on the loss dissipation, we prove the blow-up in the inter-critical regime, and the global existence in the energy subcritical case. Our results generalize and improve the ones in [9, 11, 21].

Original language	English
Pages (from-to)	3083-3098
Number of pages	16
Journal	Communications on Pure and Applied Analysis
Volume	22
Issue number	10
DOIs	https://doi.org/10.3934/cpaa.2023100
State	Published - Oct 2023

Keywords

blow-up
Damped NLS equation
global existence
loss dissipation

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title = "EXISTENCE AND NONEXISTENCE OF GLOBAL SOLUTIONS FOR TIME-DEPENDENT DAMPED NLS EQUATIONS",

abstract = "We investigate the Cauchy problem for the nonlinear Schr{\"o}dinger equation with a time-dependent linear damping term. Under non standard assumptions on the loss dissipation, we prove the blow-up in the inter-critical regime, and the global existence in the energy subcritical case. Our results generalize and improve the ones in [9, 11, 21].",

keywords = "blow-up, Damped NLS equation, global existence, loss dissipation",

author = "Makram Hamouda and Mohamed Majdoub",

year = "2023",

month = oct,

doi = "10.3934/cpaa.2023100",

language = "English",

volume = "22",

pages = "3083--3098",

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issn = "1534-0392",

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T1 - EXISTENCE AND NONEXISTENCE OF GLOBAL SOLUTIONS FOR TIME-DEPENDENT DAMPED NLS EQUATIONS

AU - Hamouda, Makram

AU - Majdoub, Mohamed

PY - 2023/10

Y1 - 2023/10

N2 - We investigate the Cauchy problem for the nonlinear Schrödinger equation with a time-dependent linear damping term. Under non standard assumptions on the loss dissipation, we prove the blow-up in the inter-critical regime, and the global existence in the energy subcritical case. Our results generalize and improve the ones in [9, 11, 21].

AB - We investigate the Cauchy problem for the nonlinear Schrödinger equation with a time-dependent linear damping term. Under non standard assumptions on the loss dissipation, we prove the blow-up in the inter-critical regime, and the global existence in the energy subcritical case. Our results generalize and improve the ones in [9, 11, 21].

KW - blow-up

KW - Damped NLS equation

KW - global existence

KW - loss dissipation

UR - https://www.scopus.com/pages/publications/85176923237

U2 - 10.3934/cpaa.2023100

DO - 10.3934/cpaa.2023100

M3 - Article

AN - SCOPUS:85176923237

SN - 1534-0392

VL - 22

SP - 3083

EP - 3098

JO - Communications on Pure and Applied Analysis

JF - Communications on Pure and Applied Analysis

IS - 10

ER -

EXISTENCE AND NONEXISTENCE OF GLOBAL SOLUTIONS FOR TIME-DEPENDENT DAMPED NLS EQUATIONS

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Keywords

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