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Threshold and strong threshold solutions of a semilinear parabolic equation. (English) Zbl 1430.35148

Summary: If \(p>1+2/n\), then the equation \(u_t-\Delta u = u^p, x\in{\mathbb R}^n,\;t>0,\) possesses both positive global solutions and positive solutions which blow up in finite time. We study the large time behavior of radial positive solutions lying on the borderline between global existence and blow-up.

MSC:

35K91 Semilinear parabolic equations with Laplacian, bi-Laplacian or poly-Laplacian
35B07 Axially symmetric solutions to PDEs
35B40 Asymptotic behavior of solutions to PDEs
35B44 Blow-up in context of PDEs
35K15 Initial value problems for second-order parabolic equations
35K57 Reaction-diffusion equations
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