Tohoku Mathematical Journal
2003
December
SECOND SERIES VOL. 55, NO. 4

Tohoku Math. J.
55 (2003), 565-581

Title BLOW-UP BEHAVIOR FOR A SEMILINEAR HEAT EQUATION WITH A NONLINEAR BOUNDARY CONDITION

Author Sheng-Chen Fu, Jong-Shenq Guo and Je-Chiang Tsai

(Received December 28, 2001, revised September 9, 2002)
Abstract. We study the blow-up behaviors of solutions of a semilinear heat equation with a nonlinear boundary condition. Under certain conditions, we prove that the blow-up point occurs only at the boundary. Then, by applying the well-known method of Giga-Kohn, we derive the time asymptotic of solutions near the blow-up time. Finally, we prove that the blow-up is complete.

2000 Mathematics Subject Classification. Primary 35K60; Secondary 34A12, 35B40, 35K20.

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