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. Birkhäuser, Basel, pp 85–110, 2006) to parabolic H-measures developed by Antonić 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 Schrödinger equation and the vibrating plate equation.

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Correspondence to Ivan Ivec.

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The authors have been supported in part by Croatian Science Foundation under projects IP-2016-06-2468 ConDyS and IP-2018-01-2449 MiTPDE.

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Ivec, I., Lazar, M. Propagation principle for parabolic H-measures. J. Pseudo-Differ. Oper. Appl. 11, 467–489 (2020). https://doi.org/10.1007/s11868-019-00289-z

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Keywords

  • Parabolic H-measures
  • Localisation principle
  • Propagation principle
  • The Schrödinger equation
  • The vibrating plate equation

Mathematics Subject Classification

  • 35K10
  • 35K25
  • 35S05
  • 46G10