Matches in SemOpenAlex for { <https://semopenalex.org/work/W2947556032> ?p ?o ?g. }
Showing items 1 to 67 of
67
with 100 items per page.
- W2947556032 abstract "This dissertation is devoted to the study of linear and nonlinear aspects of the Schrodinger-type equations [ i partial_t u + |nabla|^sigma u = F, quad |nabla| = sqrt {-Delta}, quad sigma in (0, infty).] When dollar sigma = 2 dollar, it is the well-known Schrodinger equation arising in many physical contexts such as quantum mechanics, nonlinear optics, quantum field theory and Hartree-Fock theory. When dollar sigma in (0,2) backslash {1} dollar, it is the fractional Schrodinger equation, which was discovered by Laskin (see e.g. cite{Laskin2000} and cite{Laskin2002}) owing to the extension of the Feynman path integral, from the Brownian-like to Levy-like quantum mechanical paths. This equation also appears in the water waves model (see e.g. cite{IonescuPusateri} and cite{Nguyen}). When dollar sigma = 1 dollar, it is the half-wave equation which arises in water waves model (see cite{IonescuPusateri}) and in gravitational collapse (see cite{ElgartSchlein}, cite{FrohlichLenzmann}). When dollar sigma =4 dollar, it is the fourth-order or biharmonic Schrodinger equation introduced by Karpman cite {Karpman} and by Karpman-Shagalov cite{KarpmanShagalov} taking into account the role of small fourth-order dispersion term in the propagation of intense laser beam in a bulk medium with Kerr nonlinearity. This thesis is divided into two parts. The first part studies Strichartz estimates for Schrodinger-type equations on manifolds including the flat Euclidean space, compact manifolds without boundary and asymptotically Euclidean manifolds. These Strichartz estimates are known to be useful in the study of nonlinear dispersive equation at low regularity. The second part concerns the study of nonlinear aspects such as local well-posedness, global well-posedness below the energy space and blowup of rough solutions for nonlinear Schrodinger-type equations.[...]" @default.
- W2947556032 created "2019-06-07" @default.
- W2947556032 creator A5087338257 @default.
- W2947556032 date "2018-07-10" @default.
- W2947556032 modified "2023-10-03" @default.
- W2947556032 title "Strichartz estimates and the nonlinear Schrödinger-type equations" @default.
- W2947556032 hasPublicationYear "2018" @default.
- W2947556032 type Work @default.
- W2947556032 sameAs 2947556032 @default.
- W2947556032 citedByCount "0" @default.
- W2947556032 crossrefType "dissertation" @default.
- W2947556032 hasAuthorship W2947556032A5087338257 @default.
- W2947556032 hasConcept C121332964 @default.
- W2947556032 hasConcept C134306372 @default.
- W2947556032 hasConcept C154018700 @default.
- W2947556032 hasConcept C18903297 @default.
- W2947556032 hasConcept C2777299769 @default.
- W2947556032 hasConcept C2779557605 @default.
- W2947556032 hasConcept C33923547 @default.
- W2947556032 hasConcept C37914503 @default.
- W2947556032 hasConcept C54207081 @default.
- W2947556032 hasConcept C62520636 @default.
- W2947556032 hasConcept C63036615 @default.
- W2947556032 hasConcept C83774755 @default.
- W2947556032 hasConcept C84114770 @default.
- W2947556032 hasConcept C86803240 @default.
- W2947556032 hasConceptScore W2947556032C121332964 @default.
- W2947556032 hasConceptScore W2947556032C134306372 @default.
- W2947556032 hasConceptScore W2947556032C154018700 @default.
- W2947556032 hasConceptScore W2947556032C18903297 @default.
- W2947556032 hasConceptScore W2947556032C2777299769 @default.
- W2947556032 hasConceptScore W2947556032C2779557605 @default.
- W2947556032 hasConceptScore W2947556032C33923547 @default.
- W2947556032 hasConceptScore W2947556032C37914503 @default.
- W2947556032 hasConceptScore W2947556032C54207081 @default.
- W2947556032 hasConceptScore W2947556032C62520636 @default.
- W2947556032 hasConceptScore W2947556032C63036615 @default.
- W2947556032 hasConceptScore W2947556032C83774755 @default.
- W2947556032 hasConceptScore W2947556032C84114770 @default.
- W2947556032 hasConceptScore W2947556032C86803240 @default.
- W2947556032 hasLocation W29475560321 @default.
- W2947556032 hasOpenAccess W2947556032 @default.
- W2947556032 hasPrimaryLocation W29475560321 @default.
- W2947556032 hasRelatedWork W1538375073 @default.
- W2947556032 hasRelatedWork W1981371463 @default.
- W2947556032 hasRelatedWork W2009697764 @default.
- W2947556032 hasRelatedWork W2017407604 @default.
- W2947556032 hasRelatedWork W2021137228 @default.
- W2947556032 hasRelatedWork W2048216020 @default.
- W2947556032 hasRelatedWork W2059070071 @default.
- W2947556032 hasRelatedWork W2066000472 @default.
- W2947556032 hasRelatedWork W2084178967 @default.
- W2947556032 hasRelatedWork W2094107521 @default.
- W2947556032 hasRelatedWork W2107614255 @default.
- W2947556032 hasRelatedWork W2128416297 @default.
- W2947556032 hasRelatedWork W2142979154 @default.
- W2947556032 hasRelatedWork W2329758779 @default.
- W2947556032 hasRelatedWork W2525441175 @default.
- W2947556032 hasRelatedWork W2896825857 @default.
- W2947556032 hasRelatedWork W2953198320 @default.
- W2947556032 hasRelatedWork W2963812874 @default.
- W2947556032 hasRelatedWork W3160922718 @default.
- W2947556032 hasRelatedWork W2047242608 @default.
- W2947556032 isParatext "false" @default.
- W2947556032 isRetracted "false" @default.
- W2947556032 magId "2947556032" @default.
- W2947556032 workType "dissertation" @default.