具有Neumann边界条件热方程组的爆破速度

The Blow-up Rate for a System of Heat Equations with Neumann Boundary Conditions

本文考虑具有 Ｎｅｕｍａｎｎ边界条件 ｕ／ｎ＝ｅｖ， ｖ／η＝ｅｕ在 ＳＲ ×（０，Ｔ）热方程组。ｕｔ＝△ｕ，ｖｔ=△ｖ在ＢＲ×（０，Ｔ）解的爆破性质·我们给出了爆破速度估计并证明了爆破仅在边界上发生．

This paper deals with the blow-up properties of solutions to a system of heat equations ut = △u,vt =△v in BR ×(0,T) with the Neumann boundary conditions u/ = ev, v/η= eu on SR ×[0, T). The exact blow-up rates are established. It is also proved that the blow-up will occur only at the boundary.