Using Global Invariant Manifolds to Understand Metastability in the Burgers Equation with Small Viscosity

DOI10.1137/100808836zbMath1227.35061arXiv0810.0086OpenAlexW2101272507MaRDI QIDQ3084492

C. Eugene Wayne, Margaret Beck

Publication date: 25 March 2011

Published in: SIAM Review, SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0810.0086

zbMATH Keywords

metastabilityCole-Hopf transformationscaling variablesdiffusive \(N\)-wavesself-similar diffusion wavealgebraically weighted \(L^2\) space

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Singular perturbations in context of PDEs (35B25) Stability problems for infinite-dimensional dissipative dynamical systems (37L15) Inertial manifolds and other invariant attracting sets of infinite-dimensional dissipative dynamical systems (37L25) Semilinear parabolic equations (35K58) Self-similar solutions to PDEs (35C06)

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Uses Software

• Eigtool