具可变扩散系数的椭圆-双曲方程组的全局适定性

J4 ›› 2012, Vol. 50 ›› Issue (05): 847-853.

具可变扩散系数的椭圆-双曲方程组的全局适定性

李健¹, 高文杰², 李建军³, 王增辉^1

1. 吉林农业大学信息技术学院, 长春 130118|2. 吉林大学数学学院, 长春 130012;3. 辽宁工程技术大学理学院, 辽宁阜新 123000

收稿日期:2012-02-22 出版日期:2012-09-26 发布日期:2012-09-29
通讯作者: 高文杰 E-mail:wjgao@mail.jlu.edu.cn

Global WellPosedness for an EllipticHyperbolic System with Variable Diffusion Coefficients

LI Jian¹, GAO Wenjie², LI Jianjun³, WANG Zenghui¹

1. College of Information Technology, Jilin Agricultural University, Changchun 130118, China;2. College of Mathematics, Jilin University, Changchun 130012, China;3. College of Science, Liaoning Technical University, Fuxin 123000, Liaoning Province, China

Received:2012-02-22 Online:2012-09-26 Published:2012-09-29
Contact: GAO Wenjie E-mail:wjgao@mail.jlu.edu.cn

摘要/Abstract

摘要：

运用一阶方程的特征值、椭圆方程的L^p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.

关键词: 扩散系数, 椭圆双曲方程组, 全局适定性, 自由边界问题；肿瘤；存在唯一性

Abstract:

y means of the method of characteristics for firstorder equations, the L^p 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.

Key words: diffusion coefficients, elliptichyperbolic system, global wellposedness, free boundary problem, tumor, existence and uniqueness

中图分类号:

O175.2

李健, 高文杰, 李建军, 王增辉. 具可变扩散系数的椭圆-双曲方程组的全局适定性[J]. J4, 2012, 50(05): 847-853.

LI Jian, GAO Wen-Jie, LI Jian-Jun, WANG Ceng-Hui. Global WellPosedness for an EllipticHyperbolic System with Variable Diffusion Coefficients[J]. J4, 2012, 50(05): 847-853.