The initial boundary value problem of a class of reaction-diffusion systems (coupled parabolic systems) with nonlinear coupled source terms is considered in order to classify the initial data for the global existence, finite time blowup and longtime decay of the solution. The whole study is conducted by considering three cases according to initial energy: low initial energy case, critical initial energy case and high initial energy case. For the low initial energy case and critical initial energy case the sufficient initial conditions of global existence, long time decay and finite time blowup are given to show a sharp-like condition. And for the high initial energy case the possibility of both global existence and finite time blowup is proved first, and then some sufficient initial conditions of finite time blowup and global existence are obtained respectively.
哈尔滨工程大学数学科学学院教授，博士生导师，“龙江学者”青年学者，黑龙江省数学会常务理事，黑龙江省青年学术骨干。《哈尔滨工程大学学报》编委，SCI检索JCR1区杂志Advances in Nonlinear Analysis主编，SCI检索JCR1区杂志Applied Numerical Mathematics编委，SCI检索JCR1区杂志Boundary Value Problems副主编;SCI检索JCR4区杂志Electronic Research Archive (ERA), formally known as Electronic Research Announcements in Mathematical Sciences编委；国际杂志The Annals of the University of Craiova - Mathematics and Computer Science series编委。The 10th-13th IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory学术委员会委员（Scientific Program Committee）；第十四届-第十九届，非线性偏微分方程暑期讲习班暨学术会议组织委员会委员；12th-13th Conference of the Euro-American Consortium for Promoting the Application of Mathematics in Technical and Natural Sciences组织委员会委员。