A numerical and asymptotic study in the complex plane of blow-up solutions of a semilinear parabolic PDE

Add to your list(s) Download to your calendar using vCal

• Marco Fasondini (University of Leicester)
• Tuesday 25 July 2023, 10:00-11:00
• Seminar Room 1, Newton Institute.

If you have a question about this talk, please contact nobody.

CATW04 - Complex analysis: techniques, applications and computations - perspectives in 2023

We study the singularity dynamics of blow-up solutions of the nonlinear heat equation uₜ = uₓₓ + u² in the complex x-plane through asymptotic analyses and a variety of numerical methods, namely Fourier spectral methods and numerical analytic continuation via Padé and quadratic Padé (Hermite-Padé) approximation.  We relate the PDE solution in the complex plane asymptotically to particular solutions of a second-order nonlinear ODE (which is not of Painlevé type).  The nonlinear ODE solutions are computed on multiple Riemann sheets using an adaptive Padé integrator and, at leading order, the far-field solutions are shown to be given by the (equianharmonic) Weierstrass elliptic function, which is confirmed numerically.  This is joint work with André Weideman and John King.

This talk is part of the Isaac Newton Institute Seminar Series series.

This talk is included in these lists:

• All CMS events
• Featured lists
• INI info aggregator
• Isaac Newton Institute Seminar Series
• School of Physical Sciences
• Seminar Room 1, Newton Institute
• bld31

Note that ex-directory lists are not shown.