,QUENCHING VERSUS BLOW-UP

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This paper is conceed with the semilinear heat equation ut = Δu -u-q in Ω × (0, T) under the nonlinear boundary condition × (0, T).Criteria for finite time quenching and blow-up are established, quenching and blow-up sets are discussed, and the rates of quenching and blow-up are obtained.
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