Space-time homogenization problems for porous medium equations with nonnegative initial data
Space-time homogenization problems for porous medium equations with nonnegative initial data
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发表时间：
2021-11
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通讯作者：
G. Akagi;Tomoyuki Oka
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作者：
G. Akagi;Tomoyuki Oka
.研究了多孔介质方程非负弱解的时空均匀化极限。特别是，所谓的均匀化矩阵的特征在于细胞问题的解决方案，其中急剧变化的缩放参数r > 0。在文献[1]中已经研究了类似的问题，其中由于一些实质性障碍，功率非线性的增长受到严格限制。在本文中，这些障碍将克服发展的非负弱解的梯度的局部一致估计。
. This paper concerns a space-time homogenization limit of nonnegative weak solutions to porous medium equations. In particular, the so-called homogenized matrix will be characterized in terms of solutions to cell problems, which drastically vary in a scaling parameter r > 0 . A similar problem has already been studied in [1], where the growth of the power nonlinearity is strictly restricted due to some substantial obstacles. In the present paper, such obstacles will be overcome by developing local uniform estimates for the gradients of nonnegative weak solutions.