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Information Center for Mathematical Science

논문검색

Information Center for Mathematical Science

논문검색

Tohoku Mathematical Journal. Second Series
( Vol. 55 NO.4 / (2003))
Blow-up Behavior for A Semilinear Heat Equation With A Nonlinear Boundary Condition
Sheng-Chen Fu, Jong-Shenq Guo, Je-Chiang Tsai,
Pages. 565-581
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.
Contents 1. Introduction
2. Blow-up set
3. Some a priori estimates
4. Self-similar solution
5. Time asymptotic analysis
6. Complete blow-up
Key words
Mathmatical Subject Classification 35K60, 34A12, 35B40, 35K20