Global existence and convergence to a singular steady state for a semilinear heat equation

DOI10.1017/S0308210500022113zbMath0636.35036OpenAlexW2321378920MaRDI QIDQ3775904

Andrew A. Lacey, Dimitrios E. Tzanetis

Publication date: 1987

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0308210500022113

zbMATH Keywords

blow-upinitial value problemsunbounded solutionUpper and lower solutionssingular steady stateglobally bounded

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Initial value problems for second-order parabolic equations (35K15)

Related Items (12)

Global existence and divergence of critical solutions of a non-local parabolic problem in Ohmic heating process ⋮ On the stability or instability of the singular solution of the semilinear heat equation with exponential reaction term ⋮ Total blow-up versus single point blow-up ⋮ Lower bounds of the blow-up time for reactions ⋮ Blow-up criteria for semilinear parabolic equations ⋮ Asymptotic behaviour and blow-up of some unbounded solutions for a semilinear heat equation ⋮ Finite time blowup for semilinear reactive-diffusive systems ⋮ Boundedness of global solutions of a supercritical parabolic equation ⋮ Unnamed Item ⋮ Global solutions of inhomogeneous Hamilton-Jacobi equations ⋮ Asymptotic analysis and estimates of blow-up time for the radial symmetric semilinear heat equation in the open-spectrum case ⋮ Unnamed Item

Cites Work

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• On the nonlinear equations Δ𝑢+𝑒^{𝑢}=0 and ∂𝑣/∂𝑡=Δ𝑣+𝑒^{𝑣}

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