Protocells自由边界生长模型的适定性

 研究模拟 protocells生长的自由边界问题, 此问题中控制自由边界Ω(t)移动的演化方程为V_n=－vn－βv, 其中V_n表示边界Ω(t)的法向速度, v为构造物质的密度, β为正常数。在1999年, Cui和Friedman已研究了此问题径向对称的情况。主要针对径向不对称的情况。利用Banach空间中抛物方程的抽象理论证明此问题在 little Holder空间是局部适定的。

Well-posedness for a Free Boundary Problem Modeling Protocells

A free boundary problem modeling the growth of protocells is studied, in which the evolution equation governing the motion of the free boundary Ω(t) is given by V_n=－vn－βv， where V_n denotes the normal velocity of Ω(t), v is the density of the building material, and β is a positive constant. The radially symmetric case of this problem was previously studied by Cui and Friedman in 1999. The general radially non-symmetric case is studied. With the abstract theory for parabolic differential equations in Banach spaces, the free boundary problem is locally well-posed in little Holder spaces is proved.