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Title	Interaction of Semilinear Conormal Waves (joint work with Yiran Wang)
Creator	Antonio Sa Barreto
Publisher	Banff International Research Station for Mathematical Innovation and Discovery
Date Issued	2019-04-18T08:46
Description	We study the local propagation of singularities of solutions of $P(y,D) u= f(y,u),$ in $R^3,$ where $P(y,D)$ is a second order strictly hyperbolic operator and $f\in C^\infty.$ We choose a time function $t$ for $P(y,D)$ and assume that $f(y,u)$ is supported on $t>-1$ and that for $t<-2,$ $u$ is assumed to be the superposition of three conormal waves that intersect transversally at a point $q$ with $t(q)=0.$ We show that, provided the incoming waves are elliptic conormal distributions of appropriate type and $(\p_u^3 f)(q, u(q))\not=0,$ the nonlinear interaction will produce singularities on the light cone for $P$ over $q.$ Melrose and Ritter, and Bony, had independently shown that the solution $u$ is a Lagrangian distribution of an appropriate class associated with the light cone over $q$ and we show that under this non-degeneracy condition, $u$ is an elliptic Lagrangian distribution and we compute its principal part.
Extent	40.0 minutes
Subject	Mathematics Global Analysis, Analysis On Manifolds, Dynamical Systems And Ergodic Theory, Global Analysis
Geographic Location	Banff (Alta.)
Type	Moving Image
FileFormat	video/mp4
Language	eng
Notes	Author affiliation: Purdue University
Series	BIRS Workshop Lecture Videos (Banff, Alta)
Date Available	2019-10-16
Provider	Vancouver : University of British Columbia Library
Rights	Attribution-NonCommercial-NoDerivatives 4.0 International
DOI	10.14288/1.0383404
URI	http://hdl.handle.net/2429/71923
Affiliation	Non UBC
Peer Review Status	Unreviewed
Scholarly Level	Faculty
Rights URI	http://creativecommons.org/licenses/by-nc-nd/4.0/
AggregatedSourceRepository	DSpace

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