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Propagation principle for parabolic H-measures

Journal of Pseudo-Differential Operators and Applications volume 11, pages 467–489 (2020)Cite this article

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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Authors and Affiliations

  1. Faculty of Metallurgy, University of Zagreb, Aleja narodnih heroja 3, Sisak, Croatia

    Ivan Ivec

  2. University of Dubrovnik, Ćira Carića 4, Dubrovnik, Croatia

    Martin Lazar

Authors
  1. Ivan Ivec
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  2. Martin Lazar
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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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  • DOI: https://doi.org/10.1007/s11868-019-00289-z

Keywords

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

Mathematics Subject Classification

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