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SUMMARY:A numerical and asymptotic study in the complex plane of blow-up s
 olutions of a semilinear parabolic PDE - Marco Fasondini (University of Le
 icester)
DTSTART:20230725T090000Z
DTEND:20230725T100000Z
UID:TALK202774@talks.cam.ac.uk
DESCRIPTION:We study the singularity dynamics of blow-up solutions of the 
 nonlinear heat equation uₜ = uₓₓ + u&sup2\; in the complex x-plane t
 hrough asymptotic analyses and a variety of numerical methods\, namely Fou
 rier spectral methods and numerical analytic continuation via Pad&eacute\;
  and quadratic Pad&eacute\; (Hermite-Pad&eacute\;) approximation. &nbsp\;W
 e relate the PDE solution in the complex plane asymptotically to particula
 r solutions of a second-order nonlinear ODE (which is not of Painlev&eacut
 e\; type). &nbsp\;The nonlinear ODE solutions are computed on multiple Rie
 mann sheets using an adaptive Pad&eacute\; integrator and\, at leading ord
 er\, the far-field solutions are shown to be given by the (equianharmonic)
  Weierstrass elliptic function\, which is confirmed numerically. &nbsp\;Th
 is is joint work with Andr&eacute\; Weideman and John King.
LOCATION:Seminar Room 1\, Newton Institute
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