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UID:20251227T172539EST-4896gkUuRu@132.216.98.100
DTSTAMP:20251227T222539Z
DESCRIPTION:Title:Spatiotemporal chaos and coarsening in pattern formation 
 with Galilean invariance\n\nAbstract:\n\nThe presence of continuous symmet
 ries can strongly influence the dynamics of pattern-forming systems. I wil
 l begin with an overview of pattern formation and spatiotemporal chaos in 
 the Kuramoto-Sivashinsky (KS) equation for long-wave instability\, a much-
 studied 4th-order scalar PDE in one space dimension. Of analytical interes
 t is that while solutions of the KS equation have long been known to be bo
 unded and indeed analytic\, rigorous bounds on absorbing ball radii and at
 tractor dimension which scale optimally with the system size have proved r
 emarkably difficult to achieve\; I will review the history and current sta
 tus of such bounds.\n\nMy main focus will be the Nikolaevskiy PDE\, a 6th-
 order analogue of the KS equation modelling short-wave pattern formation w
 ith Galilean invariance\, in which coupling between long-wave and pattern 
 modes leads to spatiotemporal chaos with strong scale separation. The corr
 esponding leading-order amplitude equations\, due to Matthews and Cox\, di
 splay unexpectedly rich\, strongly system-size-dependent dynamics. I will 
 describe their long-time behaviour\, which has a single stable Burgers-lik
 e viscous shock coexisting with a chaotic region\, and the coarsening and 
 collapse leading to this asymptotic state on sufficiently large domains.\n
DTSTART:20181126T210000Z
DTEND:20181126T220000Z
LOCATION:Room 1104\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue
  Sherbrooke Ouest
SUMMARY:Ralf Wittenberg (Simon Fraser)
URL:/mathstat/channels/event/ralf-wittenberg-simon-fra
 ser-291755
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