Math 790-90.01: Advanced topics mini-course on
Similarity solns for singular dynamics in PDE's
(Fall 2022) [4852]

The lectures will describe how to study dynamics leading up to singular limits in partial differential equations (finite-time blow-up, rupture, quenching, etc). For many problems, the intermediate asymptotics before singularity formation are given by self-similar solutions. Topics to be covered will include: determining similarity solutions for nonlinear PDEs, 0th, 1st and 2nd kind similarity solutions, stability analysis of self-similar dynamics, geometric effects and conserved quantities, and numerical methods for problems with finite-time singularities.

The material should be accessible to anyone with a basic background in partial differential equations.

Applications include problems in fluid dynamics, nonlinear diffusion, geometric evolution equations and models from mathematical biology.



Thomas Witelski, Professor, Dept of Math

Course materials

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