具可变扩散系数的椭圆-双曲方程组的全局适定性

摘要

运用一阶方程的特征值、椭圆方程的Lp估计、不动点方法和延拓法证明了一个具有可变扩散系数的自由边界问题当边界的药物浓度为有界连续函数时存在唯一的全局解.%By means of the method of characteristics for first-order equations, the Lp estimate for elliptic equations, the fixed point theorem and the extension method, we proved a free boundary problem with variable diffusion coefficients has a unique global solution if the initial data of the concentration of nutrient is continuous bounded function.