一类强耦合拟线性退化抛物方程组解的全局存在与非存在性  

Global Existence and Nonexistence for a Degenerate and Strongly Coupled Quasilinear Parabolic System

作　　者：韩玉柱[1] 高文杰[1] 

机构地区：[1]吉林大学数学研究所,长春130012

出　　处：《吉林大学学报（理学版）》2009年第5期859-865,共7页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:10771085);吉林大学"985工程"项目基金

摘　　要：研究一类强耦合拟线性退化抛物方程组初边值问题正古典解的局部存在、全局存在与非全局存在性.用正则化方法和先验估计证明了问题正古典解的局部存在性,并且分别给出了该问题是否存在全局古典解的充分条件.结果表明,当种群内竞争强于种群间互惠作用时,问题存在全局解;而当两种群具有强互惠作用时,所有解均为非全局的.Local existence, global existence and nonexistence of classical solutions for a degenerate and strongly coupled quasilinear parabolic system were studied. Regularization method and a prior estimate skills were used to obtain the local existence of classical solutions. Moreover, sufficient conditions were given for the existence and nonexistence of global classical solutions. The results show that the problem admits a global solution when the intra-specific competitions are strong; whereas there exists no global solution when the species are strongly mutualistic.

关 键 词：退化抛物方程组 强耦合 全局存在 非全局存在 

分 类 号：O175.2[理学—数学]