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SUMMARY:Jean-marc DELORT (Université Paris 13)
DTSTART:20201008T140000Z
DTEND:20201008T145000Z
DTSTAMP:20260423T052503Z
UID:IMS/64
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/IMS/64/">Lon
 g time dispersive estimates for perturbations of a kink solution of one di
 mensional cubic wave equations.</a>\nby Jean-marc DELORT (Université Pari
 s 13) as part of PDE seminar via Zoom\n\n\nAbstract\nA kink is a stationar
 y solution to a cubic one dimensional wave equation $(\\partial_t^2-\\part
 ial_x^2)\\phi =\\phi-\\phi^3$ that has different limits when $x$ goes to $
 -\\infty$ and $+\\infty$\, like $H(x) =\\tanh(x/\\sqrt{2})$. Asymptotic\n\
 nstability   of this solution under small odd perturbation in the energy s
 pace has been studied in a recent work of Kowalczyk\, Martel and Mu\\~noz.
  They have been able to show that the perturbation may be written as the s
 um $a(t)Y(x) +\\psi(t\,x)$\, where $Y$ is a function in Schwartz space\, $
 a(t)$ a function of time having some decay properties at\n\ninfinity\, and
  $\\psi(t\,x)$ satisfies some local in space dispersive estimate.\n\n\nThe
   main result in this talk gives\, for small odd perturbations of the kink
  that are\n\nsmooth enough and have some space decay\, explicit rates of d
 ecay for $a(t)$ and for $\\psi(t\,x)$ in the whole space-time domain inter
 sected by a strip $\\abs{t}\\leq \\epsilon^{-4+c}$\, for any $c>0$\, where
  $\\epsilon$ is the size of the initial\n\nperturbation. \n\n\nThis is joi
 nt work with Nader Masmoudi.\n
LOCATION:https://researchseminars.org/talk/IMS/64/
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