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Life span of solutions for a semilinear heat equation with initial data having positive limit inferior at infinity. (English) Zbl 1221.35076
Summary: We present a new upper bound of the life span of positive solutions of a semilinear heat equation for initial data having positive limit inferior at space infinity. The upper bound is expressed by the data in limit inferior, not in every direction, but around a specific direction. It is also shown that the minimal time blow-up occurs when initial data attains its maximum at space infinity.
MSC:
35B44Blow-up (PDE)
35K57Reaction-diffusion equations
35K58Semilinear parabolic equations
35B09Positive solutions of PDE
References:
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