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UID:c3ebeca0-5618-4baf-9042-dc9bd204e115@nexttoyou
DTSTAMP:20261105T153533Z
DTSTART:20261105T073000Z
DTEND:20261105T204500Z
SUMMARY:PDE Seminar
LOCATION:Ayres Hall 113\, 1403 Circle Drive\, Knoxville\, TN 37996
DESCRIPTION:Speaker: Prof. Atanas Stefanov\n\nhttps://www.uab.edu/cas/math
 ematics/people/faculty-directory/atanas-stefanov\n\nTitle: Kink Solutions
  for Dispersive-Diffusive PDEs: Three Short Stories\n\nAbstract: Travelin
 g kinks are special solutions to PDEs on the real line characterized by d
 istinct limiting values at the infinities. They arise naturally in combus
 tion dynamics\, invasion fronts in population biology\, water wave theory
 \, and beyond. This talk presents three recent results centered on the ex
 istence and stability of such coherent structures.\n\nIn the first story\
 , we establish the existence of kink solutions in the fractional $\\phi^4
 $ model and discuss several consequences (joint work with P. Kevrekidis).
 \n\nThe second and third stories address a fundamental question in the th
 eory of coherent structures: *are kinks dynamically stable?* That is\, do
  solutions initialized near a kink remain close to it — or to one of its 
 translates — for all time?\n\nWe answer this question for two models :\n\
 n1) the damped Boussinesq equation\,\n\n2) dispersive-diffusive Burgers m
 odels\, such as the KdV–Burgers equation.\n\nFor the Boussinesq model\, w
 e prove that the unique monotone kink is asymptotically stable via energy
  estimates and elementary spectral theory.\n\nFor KdV–Burgers\, we establ
 ish a stronger result: the monotone kink is actually an attracting set — 
 every solution\, including those arising from a large perturbation\, conv
 erges to a translate of the kink\, with explicit decay rates. This last r
 esult build\n\nhttp://next-to-u.app/events/c3ebeca0-5618-4baf-9042-dc9bd2
 04e115
URL:http://next-to-u.app/events/c3ebeca0-5618-4baf-9042-dc9bd204e115
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