论文标题
薄薄的$ 2D $ - 层被半渗透膜分开的建模扩散
Modeling diffusion in thin $2D$-layers separated by a semi-permeable membrane
论文作者
论文摘要
由具有极大核的B淋巴细胞中信号通路模型的动机，我们研究了一个问题，即在较小尺寸的区域的扩散方程中，薄薄$ 2D $域中的反应扩散方程如何近似。特别是，我们研究了近似方程中特征的传输条件如何成为极限主方程的组成部分。我们设备了一种方案，该方案通过适当重新缩放系数并为所有涉及的所有Feller Semigroup找到一个共同的参考空间，允许正式得出极限方程的形式。获得的结果，称为Feller Semigroups的收敛定理，也可以解释为潜在随机过程的弱收敛性。
Motivated by models of signaling pathways in B lymphocytes, which have extremely large nuclei, we study the question of how reaction-diffusion equations in thin $2D$ domains may be approximated by diffusion equations in regions of smaller dimensions. In particular, we study how transmission conditions featuring in the approximating equations become integral parts of the limit master equation. We device a scheme which, by appropriate rescaling of coefficients and finding a common reference space for all Feller semigroups involved, allows deriving the form of the limit equation formally. The results obtained, expressed as convergence theorems for the Feller semigroups, may also be interpreted as a weak convergence of underlying stochastic processes.
