### Fluid dynamics

Posted on 27/03/2017, in Mathematics.**Fick’s first law** relates the diffusive flux to the concentration under the assumption of steady state. It postulates that the **flux goes from regions of high concentration to regions of low concentration**, with a magnitude that is proportional to the concentration gradient (spatial derivative), or in simplistic terms the concept that a solute will move from a region of high concentration to a region of low concentration across a concentration gradient. Xem thêm wikipedia.

**Free boundary problem** vs **Moving boundary problem** : (*trong lúc đi tìm hiểu thế nào là Stefan problem thì phát hiện ra cần phải phân biệt 2 cái này*). In mathematics, a free boundary problem is a partial differential equation to be solved for both an unknown function u and an unknown domain $\Omega$. The segment $\Gamma$ of the boundary of $\Omega$ which is not known at the outset of the problem is the free boundary.

$\Rightarrow$ **Stefan problem** : the melting of ice.

Thật ra hai cái này là như nhau, nó đều chỉ vấn đề cần giải quyết là giải $u$ và $\partial\Omega$.

**Stefan problem** : Xem file ghi ngoài bằng viết tay.