Finite-dimensional leading order dynamics for the fast diffusion equation near extinction
Beomjun Choi, Christian Seis · Discrete and Continuous Dynamical Systems · 2024
The fast diffusion equation is analyzed on a bounded domain with Dirichlet boundary conditions, for which solutions are known to extinct in finite time. We construct invariant manifolds that provide a finite-dimensional approximation near the vanishing solution to any prescribed convergence rate.