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SUMMARY:Self-similar behaviour of linear kinetic equations
DTSTART:20261015T120000Z
DTEND:20261015T130000Z
DTSTAMP:20261009T022100Z
UID:indico-event-17398@indico.math.cnrs.fr
DESCRIPTION:Speakers: José Cañizo (Univiversidad de Granada)\n\nWe consi
 der linear kinetic equations of the form $\\partial_t f + \\frac{1}{\\epsi
 lon} v \\nabla_x f = \\frac{1}{\\epsilon^2} L(f)$\, for an unknown $f$ whi
 ch depends on time $t$\, position $x$ and velocity $v$\, and where $L$ is 
 a linear operator which acts only in the velocity variable\, and which typ
 ically has a probability equilibrium in $v$. Important examples include th
 e Fokker-Planck operator\, nonlocal diffusion operators\, linear BGK-type 
 operators\, or linear Boltzmann operators. This PDE typically represents a
  mesoscopic physical model\, where we keep track of the probability distri
 bution of the position and velocity of particles. It is well known that wh
 en $\\epsilon$ tends to $0$\, this type of equation has a macroscopic or d
 iffusive limit for the density $\\rho(t\,x) := \\int f(t\,x\,v) dv$\, whic
 h is either the standard heat equation\, or the fractional heat equation. 
 As a new result\, we show that for a fixed epsilon\, the behaviour of this
  equation for large times also follows the standard or fractional heat equ
 ation\, and that the long-time and small-epsilon limits are actually inter
 changeable in many cases. This is a work in collaboration with Stéphane M
 ischler (U. Paris-Dauphine) and Niccolò Tassi (U. Granada).\n\nhttps://in
 dico.math.cnrs.fr/event/17398/
LOCATION:E2290 (Tours)
URL:https://indico.math.cnrs.fr/event/17398/
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