dc.identifier.uri |
http://dx.doi.org/10.15488/3620 |
|
dc.identifier.uri |
https://www.repo.uni-hannover.de/handle/123456789/3652 |
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dc.contributor.author |
Mielke, Alexander
|
|
dc.date.accessioned |
2018-08-23T12:59:39Z |
|
dc.date.available |
2018-08-23T12:59:39Z |
|
dc.date.issued |
1999 |
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dc.identifier.citation |
Mielke, A.: Flow properties for Young-measure solutions of semilinear hyperbolic problems. In: Royal Society of Edinburgh - Proceedings A 129 (1999), Nr. 1, S. 85-123. DOI: https://doi.org/10.1017/S0308210500027487 |
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dc.description.abstract |
For hyperbolic systems in one spatial dimension ∂tu + C∂xu = f(u), u(t, x) ∈ ℝd, we study sequences of oscillating solutions by their Young-measure limit, μ, and develop tools to study the evolution of μ directly from the Young measure, v, of the initial data. For d ≤ 2 we construct a flow mapping, St, such that μ(t) = St(v) is the unique Young-measure solution for initial value v. For d ≥ 3 we establish existence and uniqueness of Young measures that have product structure, that is the oscillations in direction of the Riemann invariants are independent. Counterexamples show that neither μ nor the marginal measures of the Riemann invariants are uniquely determined from v, except if a certain structural interaction condition for f is satisfied. We rely on ideas of transport theory and make use of the Wasserstein distance on the space of probability measures. |
eng |
dc.language.iso |
eng |
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dc.publisher |
Cambridge : Cambridge University Press |
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dc.relation.ispartofseries |
Royal Society of Edinburgh - Proceedings A 129 (1999), Nr. 1 |
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dc.rights |
Es gilt deutsches Urheberrecht. Das Dokument darf zum eigenen Gebrauch kostenfrei genutzt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. Dieser Beitrag ist aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich. |
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dc.subject |
Hyperbolic Systems |
eng |
dc.subject |
Young measure |
eng |
dc.subject |
Riemann invariants |
eng |
dc.subject.ddc |
510 | Mathematik
|
ger |
dc.title |
Flow properties for Young-measure solutions of semilinear hyperbolic problems |
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dc.type |
Article |
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dc.type |
Text |
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dc.relation.issn |
03082105 |
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dc.relation.doi |
https://doi.org/10.1017/S0308210500027487 |
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dc.bibliographicCitation.issue |
1 |
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dc.bibliographicCitation.volume |
129 |
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dc.bibliographicCitation.firstPage |
85 |
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dc.bibliographicCitation.lastPage |
123 |
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dc.description.version |
publishedVersion |
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tib.accessRights |
frei zug�nglich |
|