一类非线性伪抛物型方程的初边值问题  

Initial boundary value problem of a class of nonlinear pseudoparabolic equations

作　　者：孙明丽[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：《黑龙江大学自然科学学报》2008年第3期343-346,共4页Journal of Natural Science of Heilongjiang University

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

摘　　要：研究了一类非线性伪抛物型方程的初边值问题。首先利用了经典的Galerkin方法的思想,构造了原问题的近似解,并对非线性伪抛物型方程中的非齐次项函数限定了如下条件:f′下方有界且g′上方有界,得到了近似解的几个先验估计;然后证明了原问题整体弱解的存在性与唯一性;最后利用Poincare不等式及Gronwall不等式,得到了问题整体广义解的渐近性质。A study was done on the initial boundary value problem of a class of nonlinear pseudoparabolic equation. Firstly, approximate solution of the original problem was constructed by using classical Galerkin method. Then under the condition that the non - homogeneous functionf is bounded below and g＇ is bounded above, several a priori estimation inequations were established. Furthermore, the existence and uniqueness of the global week solution were proved. Finally, the asymptotic behavior of the generalized global solution was discussed by using Poincare and Gronwall inequalities.

关 键 词：非线性伪抛物方程 初边值问题 整体弱解 存在唯一性 渐近性 

分 类 号：O175.26[理学—数学]