Porous medium equation to Hele-Shaw flow with general initial density
Porous medium equation to Hele-Shaw flow with general initial density
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DOI：
10.1090/tran/6969
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发表时间：
2015-09
期刊：
影响因子：
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通讯作者：
Inwon C. Kim;N. Požár
中科院分区：
文献类型：
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作者：
Inwon C. Kim;N. Požár
在本文中，我们研究了多孔介质方程的“刚性压力极限”，其中初始密度是一个有界、可积函数，在无穷远处具有足够的衰减。我们的特殊模型由 Pertham-Quiros-Vazquez 引入，描述了肿瘤区域的生长，并限制了最大细胞密度。在一般情况下，这扩展了 Caffarelli-Vazquez 和 Kim 先前的结果，他们将初始数据限制为紧集的特征函数。在极限情况下，得到 Hele-Shaw 型问题，其中界面运动定律反映了正细胞密度的存在对最大密度（肿瘤）区扩张的加速效应。
In this paper we study the "stiff pressure limit" of the porous medium equation, where the initial density is a bounded, integrable function with a sufficient decay at infinity. Our particular model, introduced by Perthame-Quiros-Vazquez, describes the growth of a tumor zone with a restriction on the maximal cell density. In a general context, this extends previous results of Caffarelli-Vazquez and Kim who restrict the initial data to be the characteristic function of a compact set. In the limit a Hele-Shaw type problem is obtained, where the interface motion law reflects the acceleration effect of the presence of a positive cell density on the expansion of the maximal density (tumor) zone.