Nonlinear behavior of model equations which are linearly ill-posed

DOI10.1080/03605308808820548zbMath0679.35082OpenAlexW2030437524MaRDI QIDQ4728760

J. Thomas Beale, David G. Schaeffer

Publication date: 1988

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605308808820548

zbMATH Keywords

linearizationsnonlinear diffusion equationsill-posednonlinear problemwell-posed

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Ill-posed problems for PDEs (35R25) Nonlinear higher-order PDEs (35G20)

Related Items (5)

ON THE WEAKLY NONLINEAR KELVIN–HELMHOLTZ INSTABILITY OF TANGENTIAL DISCONTINUITIES IN MHD ⋮ Nonlinear Hyperbolic Surface Waves ⋮ On nonlinear stabilization of linearly unstable maps ⋮ Short-wave instabilities and ill-posed initial value problems ⋮ Estimating forces during ploughing of a granular bed

Cites Work

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• Desingularization of periodic vortex sheet roll-up
• Existence of Infinitely Many Solutions for a Forward Backward Heat Equation
• A study of singularity formation in a vortex sheet by the point-vortex approximation
• The equations of motion of a perfect fluid with free boundary are not well posed.
• Vortex simulations of the Rayleigh–Taylor instability
• A semi-analytic approach to the self-induced motion of vortex sheets
• The spontaneous appearance of a singularity in the shape of an evolving vortex sheet

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