## 第28回　北大ＭＭＣセミナー　Homogenization of a Hele-Shaw-type problem in periodic spatiotemporal media

2014年 　 10月 3日 14時 30分 ～ 2014年 　 10月 3日 16時 00分

Norbert Pozar (金沢大学理工研究域）

Abstract: This talk concerns the homogenization limit of the Hele-Shaw problem in an inhomogeneous medium. The main new feature of this generalization of the well-known free boundary problem is the periodic dependence of the coefficient in the free boundary velocity law on time as well as on position. I will show that in the homogenization limit its solutions converge to the unique solution of a homogeneous Hele-Shaw-type problem with an anisotropic free boundary velocity law. Furthermore, the free boundaries converge with respect to the Hausdorff distance. The presented approach relies on the comparison principle structure of the Hele-Shaw problem and exploits the techniques of the theory of viscosity solutions.

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