一类描述肉芽肿生长的自由边界问题的数学分析

Analysis of a Free Boundary Problem Modeling the Granuloma Formation

摘要: 本文研究描述一类肉芽肿瘤生长的自由边界问题，它由定义在移动区域上的相互耦合的抛物型和双曲型方程组构成。我们首先将自由边界问题转换成固定边界上的问题，然后利用抛物型方程的Lp理论、双曲方程的特征线理论和Banach不动点定理证明该问题局部解的存在唯一性，最后利用先验估计得到整体解的存在唯一性。

Abstract: In this paper we study a free boundary value problem modeling the growth of Leishmaniasis. It consists of coupled parabolic equations and hyperbolic equations with moving boundary. Firstly, we convert the free boundary problem into an equivalent problem defined on fixed domain. Then we use Lp theory of parabolic equations, characteristic theory of hyperbolic equations and Banach fixed point theorem to prove existence and uniqueness of a local solution. Finally we extend this local solution to be global by employing a priori estimate.