DC FieldValueLanguage
dc.contributor.authorMugnolo, Delio-
dc.contributor.authorNoja, Diego-
dc.contributor.authorSeifert, Christian-
dc.date.accessioned2021-12-06T13:52:01Z-
dc.date.available2021-12-06T13:52:01Z-
dc.date.issued2016-08-04-
dc.identifier.citationAnalysis & PDE 11 (7): 1625-1652 11 (2018)de_DE
dc.identifier.issn1948-206Xde_DE
dc.identifier.urihttp://hdl.handle.net/11420/11142-
dc.description.abstractIn the present paper the Airy operator on star graphs is defined and studied. The Airy operator is a third order differential operator arising in different contexts, but our main concern is related to its role as the linear part of the Korteweg-de Vries equation, usually studied on a line or a half-line. The first problem treated and solved is its correct definition, with different characterizations, as a skew-adjoint operator on a star graph, a set of lines connecting at a common vertex representing, for example, a network of branching channels. A necessary condition turns out to be that the graph is balanced, i.e. there is the same number of ingoing and outgoing edges at the vertex. The simplest example is that of the line with a point interaction at the vertex. In these cases the Airy dynamics is given by a unitary or isometric (in the real case) group. In particular the analysis provides the complete classification of boundary conditions giving momentum (i.e., \$L^2\$-norm of the solution) preserving evolution on the graph. A second more general problem here solved is the characterization of conditions under which the Airy operator generates a contraction semigroup. In this case unbalanced star graphs are allowed. In both unitary and contraction dynamics, restrictions on admissible boundary conditions occur if conservation of mass (i.e., integral of the solution) is further imposed. The above well posedness results can be considered preliminary to the analysis of nonlinear wave propagation on branching structures.en
dc.language.isoende_DE
dc.publisherMathematical Sciences Publishersde_DE
dc.relation.ispartofAnalysis & PDEde_DE
dc.subjectAiry operatorde_DE
dc.subjectKdV equationde_DE
dc.subjectKrein spacesde_DE
dc.subjectQuantum graphsde_DE
dc.subjectThird-order differential operatorsde_DE
dc.subjectMathematical Physicsde_DE
dc.subjectMathematical Physicsde_DE
dc.subjectMathematics - Functional Analysisde_DE
dc.subjectMathematics - Mathematical Physicsde_DE
dc.subject47B25, 81Q35, 35Q53de_DE
dc.subject.ddc510: Mathematikde_DE
dc.titleAiry-type evolution equations on star graphsde_DE
dc.typeArticlede_DE
dc.type.diniarticle-
dcterms.DCMITypeText-
tuhh.abstract.englishIn the present paper the Airy operator on star graphs is defined and studied. The Airy operator is a third order differential operator arising in different contexts, but our main concern is related to its role as the linear part of the Korteweg-de Vries equation, usually studied on a line or a half-line. The first problem treated and solved is its correct definition, with different characterizations, as a skew-adjoint operator on a star graph, a set of lines connecting at a common vertex representing, for example, a network of branching channels. A necessary condition turns out to be that the graph is balanced, i.e. there is the same number of ingoing and outgoing edges at the vertex. The simplest example is that of the line with a point interaction at the vertex. In these cases the Airy dynamics is given by a unitary or isometric (in the real case) group. In particular the analysis provides the complete classification of boundary conditions giving momentum (i.e., \$L^2\$-norm of the solution) preserving evolution on the graph. A second more general problem here solved is the characterization of conditions under which the Airy operator generates a contraction semigroup. In this case unbalanced star graphs are allowed. In both unitary and contraction dynamics, restrictions on admissible boundary conditions occur if conservation of mass (i.e., integral of the solution) is further imposed. The above well posedness results can be considered preliminary to the analysis of nonlinear wave propagation on branching structures.de_DE
tuhh.publisher.doi10.2140/apde.2018.11.1625-
tuhh.publication.instituteMathematik E-10de_DE
tuhh.type.opus(wissenschaftlicher) Artikel-
dc.type.driverarticle-
dc.type.casraiJournal Article-
tuhh.container.issue7de_DE
tuhh.container.volume11de_DE
tuhh.container.startpage1625de_DE
tuhh.container.endpage1652de_DE
dc.identifier.arxiv1608.01461v1de_DE
dc.identifier.scopus2-s2.0-85048052004de_DE
local.status.inpressfalsede_DE
datacite.resourceTypeJournal Article-
datacite.resourceTypeGeneralText-
item.languageiso639-1en-
item.grantfulltextnone-
item.creatorOrcidMugnolo, Delio-
item.creatorOrcidNoja, Diego-
item.creatorOrcidSeifert, Christian-
item.mappedtypeArticle-
item.creatorGNDMugnolo, Delio-
item.creatorGNDNoja, Diego-
item.creatorGNDSeifert, Christian-
item.fulltextNo Fulltext-
item.openairetypeArticle-
item.openairecristypehttp://purl.org/coar/resource_type/c_6501-
item.cerifentitytypePublications-
crisitem.author.deptMathematik E-10-
crisitem.author.orcid0000-0001-9182-8687-
crisitem.author.parentorgStudiendekanat Elektrotechnik, Informatik und Mathematik-
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