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On a conjecture of De Giorgi related to homogenization
Univ Edinburgh, Sch Math, Mayfield Rd,Kings Bldg, Edinburgh EH9 3JZ, Midlothian, Scotland..
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).ORCID iD: 0000-0002-1316-7913
2017 (English)In: Annali di Matematica Pura ed Applicata, ISSN 0373-3114, E-ISSN 1618-1891, Vol. 196, no 6, p. 2167-2183Article in journal (Refereed) Published
Abstract [en]

For a periodic vector field F, let solve the dynamical system dX(epsilon)/dt = F (X-epsilon/epsilon). In (Set Valued Anal 2(1-2):175-182, 1994) Ennio De Giorgi enquiers whether from the existence of the limit one can conclude that . Our main result settles this conjecture under fairly general assumptions on F, which in some cases may also depend on t-variable. Once the above problem is solved, one can apply the result to the corresponding transport equation, in a standard way. This is also touched upon in the text to follow.

Place, publisher, year, edition, pages
Springer, 2017. Vol. 196, no 6, p. 2167-2183
Keywords [en]
Dynamical system, ODE, Transport, Homogenization, Convergence rate
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-243555DOI: 10.1007/s10231-017-0659-yISI: 000413440200013Scopus ID: 2-s2.0-85018757622OAI: oai:DiVA.org:kth-243555DiVA, id: diva2:1286890
Note

QC 20190208

Available from: 2019-02-08 Created: 2019-02-08 Last updated: 2019-02-08Bibliographically approved

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Shahgholian, Henrik

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