Blow-up phenomena for a semilinear heat equation with nonlinear boundary condition, I
Blow-up phenomena for a semilinear heat equation with nonlinear boundary condition, I
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DOI：
10.1007/s00033-010-0071-6
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发表时间：
2010-04
期刊：
影响因子：
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通讯作者：
L. Payne;G. Philippin;S. Piro
中科院分区：
文献类型：
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作者：
L. Payne;G. Philippin;S. Piro
考虑一类具有非线性边界条件的半线性热方程解的爆破问题。我们建立了关于非线性充分保证u(x，t)对所有TIMET&>0存在的条件，以及关于数据强迫解u(x，t)在某个有限的TIMET*处爆破的条件。此外，还得到了一个上界堡垒。在一些更严格的条件下，也导出了t*的下界。
We consider the blow-up of the solution to a semilinear heat equation with nonlinear boundary condition. We establish conditions on nonlinearities sufficient to guarantee thatu(x,t) exists for all timet> 0 as well as conditions on data forcing the solutionu(x,t) to blow up at some finite timet*. Moreover, an upper bound fort* is derived. Under somewhat more restrictive conditions, lower bounds for t* are also derived.