Propagation principle for parabolic H-measures

Abstract

We extend results obtained by Francfort (An introduction to H-measures and their applications. Variational problems in materials science. Birkhauser, Basel, pp 85–110, 2006) to parabolic H-measures developed by Antonic and Lazar (J Funct Anal 265:1190–1239, 2013). The well known theory of pseudodifferential operators is extended to parabolic classes of symbols and operators and used to obtain results applicable to a wide class of partial differential equations. The main result is the propagation principle which is then applied to the Schrodinger equation and the vibrating plate equation.