engleski

Transport properties for parabolic H-measures

Microlocal defect functionals (H-measures, semiclassical measures etc.) are objects which determine, in some sense, the lack of strong compactness for weakly convergent L2 sequences. More precisely, they describe the oscillation and concentration effects for quadratic quantities of weakly converging sequences. H-measures are suitable to treat problems where all partial derivatives are of the same order [3]. More recently, parabolic H-measures were introduced in order to treat 1:2 ratio between orders of partial derivatives [1]. We extend the results obtained in [2] to parabolic H-measures. The main result is propagation principle expressed in terms of the theory of pseudodifferential operators. It is then applied to the Schrodinger equation and the vibrating plate equation, with comparison to the results obtained in [1]. References [1] N. Antonić, M. Lazar, Parabolic H-measures, Journal of Functional Analysis, 265 (2013) 1190– 1239. [2] G. A. Francfort, An introduction to H-measures and their applications, Progress in nonlinear partial differential equations and their applications, 68 (2006) 85–110. [3] L. Tartar, H-measures, a new approach for studying homogenisation, oscillations and concentration effects in partial differential equations, Proceedings of the Royal Society of Edinburgh, 115A (1990) 193–230. [4] L. Tartar, H- measures and propagation effects, Rend. Lincei Mat. Appl., 28 (2017) 701–728.

parabolic H measures ; transport properties

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