Analysis and Numerical Approximation of an Integro-differential Equation Modeling Non-local Effects in Linear Elasticity
| dc.contributor.author | Emmrich, Etienne | |
| dc.contributor.author | Weckner, Olaf | |
| dc.date.accessioned | 2019-01-08T17:33:52Z | |
| dc.date.available | 2019-01-08T17:33:52Z | |
| dc.date.issued | 2007 | |
| dc.description | Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich. | de |
| dc.description | This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively. | en |
| dc.description.abstract | Long-range interactions for linearly elastic media resulting in nonlinear dispersion relations are modeled by an initial-value problem for an integro-differential equation (IDE) that incorporates non-local effects. Interpreting this IDE as an evolutionary equation of second order, well-posedness in L ∞(ℝ) as well as jump relations are proved. Moreover, the construction of the micromodulus function from the dispersion relation is studied. A numerical approximation based upon quadrature is suggested and carried out for two examples, one involving jump discontinuities in the initial data corresponding to a Riemann-like problem. | en |
| dc.identifier.eissn | 1741-3028 | |
| dc.identifier.issn | 1081-2865 | |
| dc.identifier.uri | https://depositonce.tu-berlin.de/handle/11303/8848 | |
| dc.identifier.uri | http://dx.doi.org/10.14279/depositonce-7977 | |
| dc.language.iso | en | |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | |
| dc.subject.ddc | 510 Mathematik | de |
| dc.subject.ddc | 620 Ingenieurwissenschaften und zugeordnete Tätigkeiten | de |
| dc.subject.other | long-range interactions | en |
| dc.subject.other | peridynamic theory | en |
| dc.subject.other | nonlinear dispersion relations | en |
| dc.subject.other | integro-differential equation | en |
| dc.subject.other | existence and uniqueness | en |
| dc.subject.other | jump discontinuity | en |
| dc.subject.other | numerical approximation | en |
| dc.title | Analysis and Numerical Approximation of an Integro-differential Equation Modeling Non-local Effects in Linear Elasticity | en |
| dc.type | Article | en |
| dc.type.version | publishedVersion | en |
| dcterms.bibliographicCitation.doi | 10.1177/1081286505059748 | |
| dcterms.bibliographicCitation.issue | 4 | |
| dcterms.bibliographicCitation.journaltitle | Mathematics and Mechanics of Solids | en |
| dcterms.bibliographicCitation.originalpublishername | SAGE Publications | en |
| dcterms.bibliographicCitation.originalpublisherplace | Washington, DC | en |
| dcterms.bibliographicCitation.pageend | 384 | |
| dcterms.bibliographicCitation.pagestart | 363 | |
| dcterms.bibliographicCitation.volume | 12 | |
| tub.accessrights.dnb | domain | |
| tub.affiliation | Fak. 2 Mathematik und Naturwissenschaften::Inst. Mathematik | de |
| tub.affiliation.faculty | Fak. 2 Mathematik und Naturwissenschaften | de |
| tub.affiliation.institute | Inst. Mathematik | de |
| tub.publisher.universityorinstitution | Technische Universität Berlin | de |
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