一类具有记忆项的四阶抛物型方程组的初边值问题  

Initial Boundary Value Problem of a Class of Fourth-order Parabolic Equations with Memory Terms

作　　者：李莎 杨晗[1] 高雪妍 LI Sha;YANG Han;GAO Xueyan(School of Mathematics,Southwest Jiaotong University,Chengdu 611756,China)

机构地区：[1]西南交通大学数学学院,成都611756

出　　处：《西华师范大学学报（自然科学版）》2020年第3期286-294,共9页Journal of China West Normal University(Natural Sciences)

基　　金：国家自然科学基金项目(11701477)。

摘　　要：本文研究了一类具有记忆项的四阶抛物型方程组的初边值问题。借助势阱理论,采用Galerkin方法证明了整体弱解的存在性。在整体弱解存在的前提下,利用积分不等式技术和索伯列夫嵌入定理,证明了该方程组弱解的能量呈指数衰减。最后,结合凸方法分别证明了初始能量为正或为负两种情形时弱解在有限时刻爆破,并得到了解的生命跨度的上界估计。This paper talks about the initial boundary value problem of a class of fourth-order parabolic equations with memory terms.The existence of global weak solution is obtained by potential well theory and Galerkin method. It is confirmed by integral inequality and Sobolev embedding theorem that the energy of weak solution decays exponentially under the premise of global weak solution. At last,the finite blow-up of the weak solution in the situation of positive and negative initial energy is proved by convex method and the upper bound estimation of the life-span is also given.

关 键 词：四阶抛物型方程组 势阱 整体解 能量衰减 爆破 生命跨度 

分 类 号：O175.26[理学—数学]