Blow-up of solutions for semilinear fractional Schrödinger equations

A. Z. Fino; I. Dannawi; M. Kirane

doi:10.1216/JIE-2018-30-1-67

Blow-up of solutions for semilinear fractional Schrödinger equations

A. Z. Fino, I. Dannawi, M. Kirane

Mathematics

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

7 Scopus citations

Abstract

We consider the Cauchy problem in R^N, N ≥ 1, for the semi-linear Schrödinger equation with fractional Laplacian. We present the local well-posedness of solutions in H^α/2(R^N), 0 < α < 2. We prove a finite-time blow-up result, under suitable conditions on the initial data.

Original language	British English
Pages (from-to)	67-80
Number of pages	14
Journal	Journal of Integral Equations and Applications
Volume	30
Issue number	1
DOIs	https://doi.org/10.1216/JIE-2018-30-1-67
State	Published - 2018

Keywords

Blow-up
Fractional Laplacian
Schrödinger equations

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10.1216/JIE-2018-30-1-67

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title = "Blow-up of solutions for semilinear fractional Schr{\"o}dinger equations",

abstract = "We consider the Cauchy problem in RN, N ≥ 1, for the semi-linear Schr{\"o}dinger equation with fractional Laplacian. We present the local well-posedness of solutions in Hα/2(RN), 0 < α < 2. We prove a finite-time blow-up result, under suitable conditions on the initial data.",

keywords = "Blow-up, Fractional Laplacian, Schr{\"o}dinger equations",

author = "Fino, {A. Z.} and I. Dannawi and M. Kirane",

note = "Publisher Copyright: {\textcopyright} 2018 Rocky Mountain Mathematics Consortium.",

year = "2018",

doi = "10.1216/JIE-2018-30-1-67",

language = "British English",

volume = "30",

pages = "67--80",

journal = "Journal of Integral Equations and Applications",

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T1 - Blow-up of solutions for semilinear fractional Schrödinger equations

AU - Fino, A. Z.

AU - Dannawi, I.

AU - Kirane, M.

PY - 2018

Y1 - 2018

N2 - We consider the Cauchy problem in RN, N ≥ 1, for the semi-linear Schrödinger equation with fractional Laplacian. We present the local well-posedness of solutions in Hα/2(RN), 0 < α < 2. We prove a finite-time blow-up result, under suitable conditions on the initial data.

AB - We consider the Cauchy problem in RN, N ≥ 1, for the semi-linear Schrödinger equation with fractional Laplacian. We present the local well-posedness of solutions in Hα/2(RN), 0 < α < 2. We prove a finite-time blow-up result, under suitable conditions on the initial data.

KW - Blow-up

KW - Fractional Laplacian

KW - Schrödinger equations

UR - http://www.scopus.com/inward/record.url?scp=85045190994&partnerID=8YFLogxK

U2 - 10.1216/JIE-2018-30-1-67

DO - 10.1216/JIE-2018-30-1-67

M3 - Article

AN - SCOPUS:85045190994

SN - 0897-3962

VL - 30

SP - 67

EP - 80

JO - Journal of Integral Equations and Applications

JF - Journal of Integral Equations and Applications

IS - 1

ER -

Blow-up of solutions for semilinear fractional Schrödinger equations

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Keywords

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