一类通量饱和扩散方程的最优等待时间界
Optimal waiting time bounds for some flux-saturated diffusion equations
摘要：
考虑两类通量饱和扩散方程的Cauchy问题。在任意的空间维上，给出了判别等待时间现象发生与否的初始数据增长的最优条件。我们还证明了最优上界的等待时间。我们的论点是基于引进适当的家庭的子解和比较结果的一般类的通量饱和扩散方程。
英文摘要：
We consider the Cauchy problem for two prototypes of flux-saturated diffusion equations. In arbitrary space dimension, we give an optimal condition on the growth of the initial datum which discriminates between occurrence or nonoccurrence of a waiting time phenomenon. We also prove optimal upper bounds on the waiting time. Our argument is based on the introduction of suitable families of subsolutions and on a comparison result for a general class of flux-saturated diffusion equations.
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