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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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##### References:
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