Naslov
A parabolic variant of H-measures

Autori
Lazar, Martin

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

Izvornik
A conference on Applied Analysis / Fonseca, Irene i dr. - Pittsburgh (PA), 2006, 16-16

Skup
A conference on Applied Analysis

Mjesto i datum
Pittsburgh (PA), Sjedinjene Američke Države, 19.10.2006. - 21.10.2006

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Nije recenziran

Ključne riječi
variant H-measures; heat equation; Schrodinger equation

Sažetak
H-measures have been introduced as a tool for studying quadratic terms of weakly converging $L^2$ sequences. As such, they have proved appropriate for exploring limits of energy terms. Due to special scaling of the dual variable ($\xi/|\xi|$) included in the definition of H-measures, they have mostly been used for hyperbolic equations and systems. The above scaling turned out to be unsuitable for the applications to equations of parabolic type. Therefore, a variant of H-measures has been developed, containing a different scaling for the dual variable, which is better suited to the equations of this type. The obtained results give a good example of differences between the original H-measures and its variants. While in the first case the results have turned out to be trivial with H-measures supported in two points (North/South pole) of dual space, a new variant gives measures supported on the curves, thus enabling a study of propagation phenomena. The explicit relation between macroscopic energy dissipation term and given data is obtained. Applications to the heat and Schroedinger equation will be presented.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA