一类具交错扩散的强耦合退化抛物方程组解的整体存在与非存在性  

GLOBAL EXISTENCE AND NONEXISTENCE OF SOLUTIONS FOR A DEGENERATE AND STRONGLY COUPLED PARABOLIC SYSTEM WITH CROSSWISE DIFFUSION

作　　者：高景璐[1] 韩玉柱[1] 高文杰[1] 

机构地区：[1]吉林大学数学学院,吉林长春130012

出　　处：《数学杂志》2014年第5期947-958,共12页Journal of Mathematics

基　　金：国家自然科学基金资助(10771085;11271154);吉林大学"985工程"项目基金资助;吉林大学研究生创新基金

摘　　要：本文研究了一类具交错扩散的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,整体存在与非整体存在性.利用正则化方法和先验估计技巧证明了该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整体古典解的充分条件.结果表明当种群内竞争强于种群间互惠作用时,此问题存在整体解;而当两种群具有强互惠作用时,所有解都是非整体的.In this paper, the authors investigate a degenerate and strongly coupled parabolic system that can be used to describe a cooperating two-species model with crosswise diffusion. Local existence of positive classical solutions is proved by using the method of regularization and a prior estimates. Moreover, the authors also give some sufficient conditions for the existence and non-existence of global solutions, respectively. 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 整体存在 非整体存在 交错扩散 

分 类 号：O175.2[理学—数学]