A parabolic variant of H-measures |
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Authors: | Nenad Antonić Martin Lazar |
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Institution: | (1) Department of Mathematics, University of Zagreb, Bijenička cesta 30, Zagreb, Croatia;(2) University of Dubrovnik, Ćira Carića 4, Dubrovnik, Croatia |
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Abstract: | H-measures, as originally introduced by Luc Tartar and Patrick Gérard, are suited to hyperbolic problems. However, they turned out not to be well adjusted to the study of parabolic equations. A variant of H-measures is proposed, which is much better adapted to such kind of problems. We present the new parabolic scaling and the main ingredients for the proof of existence of the new variant. Some applications to the Schrödinger equation and vibrating plate equation are shown, together with an outlook to possible applications in other problems. |
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Keywords: | Variant H-measure Oscillation Parabolic equation Schr?dinger’ s equation Vibrating plate equation |
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