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一类带有对数非线性项的热方程的梯度爆破问题
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Abstract:
我们考虑了具有一般对数非线性项的一维半线性热方程的梯度爆破问题，也就是方程解本身有界，但解的梯度会趋于无穷。通过尺度变换和抛物估计，得到了解梯度的一个上界和下界。最后给出了一个特殊例子来验证。
We considered the gradient blow up problem of the one-dimensional semi-linear heat equation with general logarithmic nonlinear term, which the solution of the equation is bounded but the gradient of the solution becomes unbounded. By the rescaling method and parabolic estimates, the upper and lower bounds of gradient blow up rate are established. Furthermore, an example is given to illustrate.
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