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

Choi, Beomjun; Seis, Christian

Research article (journal) | Peer reviewed

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.

Details about the publication

Journal: Discrete and Continuous Dynamical Systems - Series A (Discrete Contin. Dynam. Systems A)

Volume: 44

Issue: 9

Page range: 2697-2712

Status: Published

Release year: 2024

Language in which the publication is written: English

DOI: 10.3934/dcds.2024043

Link to the full text: https://arxiv.org/abs/2308.15032

Keywords: Fast difusion; Dirichlet problem; finite time extinction; large time asymptotics

Authors from the University of Münster

Seis, Christian

Professorship for applied mathematics (Prof. Seis)