### 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.

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