Non-existence of local solutions of semilinear heat equations of Osgood type in bounded domains

DOI10.1016/j.crma.2014.05.010zbMath1297.35114OpenAlexW2078128198MaRDI QIDQ404424

Robert Laister, James C. Robinson, Mikołaj Sierżęga

Publication date: 4 September 2014

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: http://eprints.uwe.ac.uk/23149/7/prodigal-cras.pdf

zbMATH Keywords

Dirichlet boundary conditionsOsgood conditionimmediate blow-up

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Blow-up in context of PDEs (35B44) Semilinear parabolic equations (35K58)

Related Items (3)

Existence and uniqueness of global solutions to the stochastic heat equation with superlinear drift on an unbounded spatial domain ⋮ A complete characterisation of local existence for semilinear heat equations in Lebesgue spaces ⋮ A necessary and sufficient condition for uniqueness of the trivial solution in semilinear parabolic equations

Cites Work

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• Ill-posedness of the Navier-Stokes equations in a critical space in 3D
• Semilinear evolution equations in Banach spaces
• Non-existence of local solutions for semilinear heat equations of Osgood type
• No LocalL¹Solution for a Nonlinear Heat Equation

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