"Non UBC"@en .
"DSpace"@en .
"Antonio Sa Barreto"@en .
"2019-10-16T08:16:09Z"@en .
"2019-04-18T08:46"@en .
"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."@en .
"https://circle.library.ubc.ca/rest/handle/2429/71923?expand=metadata"@en .
"40.0 minutes"@en .
"video/mp4"@en .
""@en .
"Author affiliation: Purdue University"@en .
"Banff (Alta.)"@en .
"10.14288/1.0383404"@en .
"eng"@en .
"Unreviewed"@en .
"Vancouver : University of British Columbia Library"@en .
"Banff International Research Station for Mathematical Innovation and Discovery"@en .
"Attribution-NonCommercial-NoDerivatives 4.0 International"@en .
"http://creativecommons.org/licenses/by-nc-nd/4.0/"@en .
"Faculty"@en .
"BIRS Workshop Lecture Videos (Banff, Alta)"@en .
"Mathematics"@en .
"Global Analysis, Analysis On Manifolds, Dynamical Systems And Ergodic Theory, Global Analysis"@en .
"Interaction of Semilinear Conormal Waves (joint work with Yiran Wang)"@en .
"Moving Image"@en .
"http://hdl.handle.net/2429/71923"@en .