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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:A numerical and asymptotic study in the complex pl
 ane of blow-up solutions of a semilinear parabolic
  PDE - Marco Fasondini (University of Leicester)
DTSTART;TZID=Europe/London:20230725T100000
DTEND;TZID=Europe/London:20230725T110000
UID:TALK202774AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/202774
DESCRIPTION:We study the singularity dynamics of blow-up solut
 ions of the nonlinear heat equation uₜ = uₓₓ + u&s
 up2\; in the complex x-plane through asymptotic an
 alyses and a variety of numerical methods\, namely
  Fourier spectral methods and numerical analytic c
 ontinuation via Pad&eacute\; and quadratic Pad&eac
 ute\; (Hermite-Pad&eacute\;) approximation. &nbsp\
 ;We relate the PDE solution in the complex plane a
 symptotically to particular solutions of a second-
 order nonlinear ODE (which is not of Painlev&eacut
 e\; type). &nbsp\;The nonlinear ODE solutions are 
 computed on multiple Riemann sheets using an adapt
 ive Pad&eacute\; integrator and\, at leading order
 \, the far-field solutions are shown to be given b
 y the (equianharmonic) Weierstrass elliptic functi
 on\, which is confirmed numerically. &nbsp\;This i
 s joint work with Andr&eacute\; Weideman and John 
 King.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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