engleski

Propagation principle for parabolic H-measures

Microlocal defect functionals (H-measures, H- distributions, semiclassical measures etc.) are objects which determine, in some sense, the lack of strong compactness for weakly convergent Lp sequences. H-measures are suitable to treat problems where all partial derivatives are of the same order [3]. Recently, parabolic H- measures are introduced in order to treat 1:2 ratio between orders of partial derivatives [1]. We extend results obtained in [2] to parabolic H-measures. The main result is propagation principle expressed in terms of the theory of pseudodi erential operators. It is then applied to the Schrodinger equation and the vibrating plate equation, with comparison to the results obtained in [1]. The talk is based on collaboration with Martin Lazar. [1] Antonic, N., Lazar, M.: Parabolic H-measures, Journal of Functional Analysis 265 (2013), 1190{; ; 1239. [2] Francfort, G. A.: An introduction to H-measures and their applications, Progress in nonlinear partial di erential equations and their applications 68 (2006), 85{; ; 110. [3] Tartar, L.: H-measures, a new approach for studying homogenisation, oscillations and concen- tration e ects in partial di erential equations, Proceedings of the Royal Society of Edinburgh 115A (1990), 193{; ; 230.

parabolic H-measures

nije evidentirano