Propagation principle for parabolic H-measures. (English) Zbl 1446.35275
Summary: We extend results obtained by G. A. Francfort [Prog. Nonlinear Differ. Equ. Appl. 68, 85–110 (2006; Zbl 1129.35002)] to parabolic H-measures developed by N. Antonić and M. Lazar [J. Funct. Anal. 265, No. 7, 1190–1239 (2013; Zbl 1286.35009)]. 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.
MSC:
| 35S05 | Pseudodifferential operators as generalizations of partial differential operators |
| 35K10 | Second-order parabolic equations |
| 35K25 | Higher-order parabolic equations |
| 35Q41 | Time-dependent Schrödinger equations and Dirac equations |
| 46G10 | Vector-valued measures and integration |
Keywords:
parabolic H-measures; localisation principle; propagation principle; Schrödinger equation; vibrating plate equationReferences:
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