Department of

Mathematics


Seminar Calendar
for Turing bifurcation in systems with conservation laws events the year of Tuesday, August 9, 2022.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Friday, April 8, 2022

1:00 pm in 147 Altgeld Hall,Friday, April 8, 2022

Graduate Analysis Seminar

Aric Wheeler (Indiana University)

Abstract: Generalizing results of Matthews-Cox/Sukhtayev for a model reaction-diffusion equation, we derive and rigorously justify weakly nonlinear amplitude equations governing general Turing bifurcation in the presence of conservation laws. In the nonconvective, reaction-diffusion case, this is seen similarly as in Matthews-Cox, Sukhtayev to be a real Ginsburg-Landau equation weakly coupled with a diffusion equation in a large-scale mean-mode vector comprising variables associated with conservation laws. In the general, convective case, by contrast, the amplitude equations consist of a complex Ginsburg-Landau equation weakly coupled with a singular convection-diffusion equation featuring rapidly-propagating modes with speed $\sim 1/\epsilon$ where $\epsilon$ measures amplitude of the wave as a disturbance from a background steady state. Applications are to biological morphogenesis, in particular vasculogenesis, as described by the Murray-Oster and other mechanochemical/hydrodynamical models. This work is joint with Kevin Zumbrun.