Finite-dimensional leading order dynamics for the fast diffusion equation near extinction

Published 29 Aug 2023 in math.AP | (2308.15032v2)

Abstract: 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.

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