高压氧疗法应用于慢性伤口问题解的存在唯一性

摘要

A mathematical model of hyperbaric oxygen therapy for chronic wound healing is studied.This model contains a nonlinear second-order parabolic equation describing the concentration of oxygen diffusion,a nonlinear first-order hyperbolic equation for capillary tip density and an ordinary differential equation for blood vessel density.The existence and uniqueness of the global solution is proved by applying the characteristic theory of hyperbolic equation,the Lp-theory,H(o)lder-estimate theory and Banach fixed point theorem.%研究一个高压氧治疗对慢性伤口愈合问题的数学模型.该模型包含了描述氧扩散浓度的非线性二阶抛物型方程、关于毛细管尖端密度的非线性一阶双曲型方程以及一个描述血管密度的常微分方程.通过应用双曲方程的特征理论、Lp估计、H(o)lder估计以及Banach不动点定理证明了这个问题整体解的存在唯一性.