磷脂酰肌醇蛋白聚糖存在下的形态发生素转运模型
A model of morphogen transport in the presence of glypicans I
摘要：
我们分析了一个一维版本的模型形态运输，生物过程中管理细胞分化。该模型是由Hufnagel等提出的，用来描述果蝇翅盘内形态梯度的形成。在数学上，该模型是一个由两个抛物型偏微分方程和三个常微分方程组成的反应扩散方程系统。配体的来源是由狄拉克三角洲模拟。利用半群方法和$L_1$技巧证明了该系统的适定性和唯一定态。所有的结果证明，而不施加任何人为的限制的参数范围。
英文摘要：
We analyze a one dimensional version of a model of morphogen transport, a biological process governing cell differentiation. The model was proposed by Hufnagel et al. to describe the forming of morphogen gradient in the wing imaginal disc of the fruit fly. In mathematical terms the model is a system of reaction-diffusion equations which consists of two parabolic PDE's and three ODE's. The source of ligands is modelled by a Dirac Delta. Using semigroup approach and $L_1$ techniques we prove that the system is well-posed and possesses a unique steady state. All results are proved without imposing any artificial restrictions on the range of parameters.
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