一类非线性反应扩散耦合系统的整体解和爆破  

Global Solution and Blow-Up for a Class of Nonlinear Reaction Diffusion Coupled Systems

作　　者：樊佳幸 

机构地区：[1]西南交通大学数学学院,四川 成都

出　　处：《应用数学进展》2021年第1期189-202,共14页Advances in Applied Mathematics

摘　　要：本文研究一类带有扩散项的非线性抛物方程组的初边值问题,借助Sobolev嵌入定理,Gagliardo-Niren- berg不等式,利用Galerkin方法,建立了弱解整体存在和爆破的充分条件,结合伯努利不等式得到了弱解整体存在时的有界性。In this paper, the initial boundary value problem for a class of Nonlinear Parabolic Equations with diffusion term is studied. By means of Sobolev embedding theorem, Gagliardo Nirenberg inequality and Galerkin method, sufficient conditions for the global existence and blow up of weak solutions are established. The boundedness of global existence of weak solutions is obtained by combining Bernoulli inequality.

关 键 词：非线性抛物方程组 GALERKIN方法 整体解 爆破 

分 类 号：O17[理学—数学]