具有非局部边界的退化抛物方程组的爆破解  

BLOW-UP SOLUTIONS TO DEGENERATE PARABOLIC EQUATIONS WITH NONLOCAL BOUNDARY

作　　者：杨婕 刘丙辰 张长城 

机构地区：[1]中国石油大学(华东)理学院,山东青岛266580

出　　处：《数学杂志》2017年第6期1275-1286,共12页Journal of Mathematics

基　　金：国家自然科学基金(11201483);山东省自然科学基金(ZR2016AM12);中央高校基本科研业务费专项资金(15CX08011A)

摘　　要：本文研究了具有非局部边界条件和非局部源的退化抛物方程组的弱解问题.利用基于比较原理的上下解的方法,在权函数和初始条件的假设下,获得了该方程组问题的爆破临界指标.此外,还获得了同时爆破解趋于爆破时间时的渐近行为,推广了已有的结果.In this paper, we consider the weak solutions of the degenerate paraoonc equations coupled via nonlocal sources, subject to nonlocal boundary conditions. By using the comparison principle, the critical blow-up exponent is obtained under the help of the weighted functions and the initial data. Moreover, asymptotic behavior near blow-up time is obtained for simultaneous blow-up solutions, which extends the known results in the previous paper.

关 键 词：退化抛物方程组 临界指标 渐近行为 非局部边界 

分 类 号：O175.29[理学—数学]