DC Field | Value | Language |
---|---|---|
dc.contributor.author | 황경하 | en_US |
dc.date.accessioned | 2014-12-01T11:48:22Z | - |
dc.date.available | 2014-12-01T11:48:22Z | - |
dc.date.issued | 2012 | en_US |
dc.identifier.other | OAK-2014-01196 | en_US |
dc.identifier.uri | http://postech.dcollection.net/jsp/common/DcLoOrgPer.jsp?sItemId=000001396260 | en_US |
dc.identifier.uri | https://oasis.postech.ac.kr/handle/2014.oak/1698 | - |
dc.description | Doctor | en_US |
dc.description.abstract | In this dissertation we consider for the fractional Schrödinger equationiut = (-Δ)^α/2 u + F(u) in R^1+n, n ≥ 1with the Lévy index 1 < α < 2 and the nonlinearity F(u) = λ(jxj^-ν*juj^2)u | en_US |
dc.description.abstract | 0 < ν < n.In Chapter 1 we study the Cauchy problem for the fractional Schröodinger equation. We prove the existence and uniqueness of local and global solutionsfor certain α and ν. We also remark on finite time blowup of solutions whenλ = -1.In Chapter 2 we develop a profile decomposition of fractional Schröodingerequation with Lévvy index 1 < α < 2. One the main difficulty is the non-locality of fractional operator which causes the lack of Galilean invariance.The second one is the regularity loss of Strichartz estimate stemming from thelow index α < 2. To overcome these difficulties we assume radial symmetry and use the recently developed Strichartz estimates. We will apply the profile decomposition to the blowup profile of fractional Hartree equations. | en_US |
dc.language | eng | en_US |
dc.publisher | 포항공과대학교 | en_US |
dc.rights | BY_NC_ND | en_US |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/2.0/kr | en_US |
dc.title | 하트리유형의 비선형 분수슈뢰딩거 방정식에 관하여 | en_US |
dc.title.alternative | On fractional Schrodinger equations with Hartree type nonlinearity | en_US |
dc.type | Thesis | en_US |
dc.contributor.college | 일반대학원 수학과 | en_US |
dc.date.degree | 2012- 8 | en_US |
dc.contributor.department | 포항공과대학교 | en_US |
dc.type.docType | Thesis | - |
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