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2013•Proceedings of the Japan Academy Series A Mathematical SciencesOpen access

Life span of solutions for a quasilinear parabolic equation with initial data having positive limit inferior at infinity

Takefumi Igarashi

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Abstract

We present a new upper bound of the life span of positive solutions of a quasilinear parabolic equation for the 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 the initial data attain its maximum at space infinity.

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We present a new upper bound of the life span of positive solutions of a quasilinear parabolic equation for the 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 the initial data attain its maximum at space infinity.

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Available abstract

We present a new upper bound of the life span of positive solutions of a quasilinear parabolic equation for the 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 the initial data attain its maximum at space infinity.

Key concepts: Infinity, Limit (mathematics), Life span, Span (engineering), Mathematics, Mathematical analysis, Upper and lower bounds, Space (punctuation)

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