An ODE approach to the multiplicity of self-similar solutions for semi-linear heat equations

DOI10.1017/S0308210500004741zbMath1112.35100MaRDI QIDQ3411833

Yūki Naito

Publication date: 30 November 2006

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

zbMATH Keywords

shooting methodsingular initial data

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Initial value problems for second-order parabolic equations (35K15)

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Existence of peaking solutions for semilinear heat equations with blow-up profile above the singular steady state ⋮ A singular solution with smooth initial data for a semilinear parabolic equation ⋮ Quasi self-similarity and its application to the global in time solvability of a superlinear heat equation ⋮ Existence and blow-up of solutions in Hénon-type heat equation with exponential nonlinearity ⋮ Global existence and blow-up of solutions for the heat equation with exponential nonlinearity ⋮ Selfsimilar expanders of the harmonic map flow ⋮ Unnamed Item ⋮ The role of forward self-similar solutions in the Cauchy problem for semilinear heat equations ⋮ Existence and multiplicity of self-similar solutions for heat equations with nonlinear boundary conditions ⋮ Asymptotically self-similar behaviour of global solutions for semilinear heat equations with algebraically decaying initial data ⋮ A Liouville theorem for ancient solutions to a semilinear heat equation and its elliptic counterpart ⋮ Convergence of anisotropically decaying solutions of a supercritical semilinear heat equation ⋮ Homoclinic and heteroclinic orbits for a semilinear parabolic equation

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