A multi-dimensional blow-up problem due to a concentrated nonlinear source in $\mathbb {R}^{N}$

DOI10.1090/S0033-569X-2011-01219-3zbMath1233.35119OpenAlexW1592568187MaRDI QIDQ3015261

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Publication date: 11 July 2011

Published in: Quarterly of Applied Mathematics (Search for Journal in Brave)

Full work available at URL: http://www.ams.org/journals/qam/2011-69-02/S0033-569X-2011-01219-3/home.html

zbMATH Keywords

existenceuniquenessblow up

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Blow-up in context of PDEs (35B44) Semilinear parabolic equations (35K58) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (3)

Existence of a solution for the problem with a concentrated source in a subdiffusive medium ⋮ Existence of solution for the problem with a concentrated source in a subdiffusive medium ⋮ Quenching criteria for a parabolic problem due to a concentrated nonlinear source in an infinite strip

Cites Work

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• Existence and nonexistence of global solutions for \(u_ t = \Delta u + a(x)u^ p\) in \(\mathbb{R}^ d\)
• Classes of solutions of linear systems of partial differential equations of parabolic type
• A multi-dimensional quenching problem due to a concentrated nonlinear source in \(\mathbb R^N\)
• Multi-dimensional explosion due to a concentrated nonlinear source
• A criterion for a multi-dimensional explosion due to a concentrated nonlinear source
• Boundary Value Problems of Mathematical Physics: Volume 2
• Quenching for a degenerate parabolic problem due to a concentrated nonlinear source

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