This article is concerned with the existence of a weak solution to the initial boundary problem for a cross-diffusion system which arises in the study of two cell population growth. The mathematical challenge is due to the fact that the coefficient matrix is non-symmetric and degenerate in the sense that its determinant is $ 0 $. The existence assertion is established by exploring the fact that the total population density satisfies a porous media equation.

中文翻译：

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控制两个细胞群体运动的模型的整体存在定理

本文关注的是交叉扩散系统的初始边界问题的弱解的存在，该问题在研究两个细胞种群增长时出现。数学上的挑战是由于以下事实：系数矩阵是非对称的，并且在其行列式为$ 0 $的意义上退化。存在断言是通过探索总人口密度满足多孔介质方程的事实而建立的。