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A bound for global solutions of semilinear heat equations. (English) Zbl 0595.35057
The author proves that every global (classical) solution of equation \(u_ t=\Delta u+u^ p\) in a bounded domain in \(R^ n\) is bounded by a constant depending only on the sup-norm of the initial data if \(n/2<(p+1)/(p-1).\)
Reviewer: B.Nowak

MSC:
35K55 Nonlinear parabolic equations
35K25 Higher-order parabolic equations
35B35 Stability in context of PDEs
35K15 Initial value problems for second-order parabolic equations
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