A bound for global solutions of semilinear heat equations. (English) Zbl 0595.35057

Giga, Yoshikazu

Commun. Math. Phys. 103, 415-421 (1986).

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

Keywords:

global solutions; semilinear heat equations; initial-boundary; value problem; Dirichlet boundary condition

References:

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