Naslov
Comparison of H-measures and semiclassical measures

Autori
Antonić, Nenad ; Erceg, Marko ; Lazar, Martin

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
Eight Conference on Applied Mathematics and Scientific Computing, Šibenik, 2013. / - , 2013, 1-1

Skup
ApplMath13 - Conference on Applied Mathematics and Scientific Computing

Mjesto i datum
Šibenik, Hrvatska, 10.06.2013. - 14.06.2013

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Domaća recenzija

Ključne riječi
H-measures ; semiclassical measures

Sažetak
Semiclassical measures were introduced by Patrick Gérard (1991), but are also known under the name of Wigner measures as Pierre Louis Lions and Thierry Paul gave a different construction using the Wigner transform. They are mathematical objects used in the study of high-frequency limits in continuum and quantum mechanics. In contrast to the H-measures, they are tailored to deal with problems which have a characteristic length (e.g. thickness of a plate). Recently, Luc Tartar extended semiclassical measures to a functional on continuous functions on a compactification of $R^d\setminus\{; ; ; 0\}; ; ; $. Our aim is to study more deeply this extension and its relation to H-measures. It is known that for an $\epsilon_n$-oscillatory sequence we can obtain that the corresponding H-measure and the semiclassical measure are equal, but for the above extension such assumption is superfluous, while the proof is simpler. In particular, we shall study PDEs with characteristic length tending to zero to emphasize situations where H-measures and semiclassical measures do not give the same information, and where with semiclassical measures we indeed get something more.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA