两类非线性拟抛物方程解的有限时间爆破和长时间行为  

On Finite Time Blow up and Long Time Behaviours of Solutions for Two Classes of Nonlinear Pseudoparabolic Equations

作　　者：徐润章[1] 刘亚成[1] 

机构地区：[1]哈尔滨工程大学理学院,哈尔滨150001

出　　处：《工程数学学报》2005年第5期800-806,共7页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(10271034);哈尔滨工程大学基础研究基金(HEUF04012).

摘　　要：本文研究两类非线性拟抛物方程的初边值问题,它们包括了GBBM方程,Sobolev-Galpern方程,多维粘性扩散方程及半线性拟抛物方程作为特殊情形。对这两类方程我们分别采用积分估计方法和特征函数法证明了,当方程的非线性项满足某些条件时,问题的解按时间t的指数形式衰减为零,而当方程的非线性项满足另外某些条件时,问题的解在有限时间内爆破。本文从实质上改进和推广了已有结果。We study the initial boundary value problem of nonlinear pseudoparabolic equations which includes GBBM equations, Sobolov-Galpern equations, multidimensional viscodiffusion equations and semilinear pseudoparabolic equations as special cases. For these two classes of equations, by using integral estimate method and eigenfunction method, respectively, we prove that the solutions of problems decay to zero according to exponent of t, when the nonlinear terms satisfy some conditions, and the solutions blow up in finite time when the nonlinear terms of equations satisfy some other conditions. The known results are improved and generalized.

关 键 词：非线性拟抛物方程 初边值 长时间行为 爆破 

分 类 号：O175.26[理学—数学]