一类三阶非线性伪抛物方程的初边值问题  

THE INITIAL-BOUNDARY PROBLEM FOR A CLASS OF THE THIRD ORDER NON-LINEAR PSEUDOPARABOLIC EQUATIONS

作　　者：吴建成[1] 黄清龙[2] 

机构地区：[1]江苏工业学院信息科学与工程学院,常州213164 [2]江苏工业学院数理学院,常州213164

出　　处：《系统科学与数学》2008年第5期635-640,共6页Journal of Systems Science and Mathematical Sciences

摘　　要：非线性伪抛物方程由于其来源于一些重要的物理过程而成为研究热点.对于一类三阶非线性伪抛物方程的初边值问题,给出了Hilbert空间中相应的强制不等式,利用同胚理论及推广的反函数定理,得到了非线性方程初边值问题解的大范围存在定理.对于相应的半线性方程给出了初边值问题解的大范围存在性、唯一性定理.Non-linear pseudoparabolic equation is currently of much interest because it arises in a variety of important physical processes. In this article, by using homeomorphism method, the above problem is investigated. An existence theorem of solutions for the problem is given. Also, an existence and uniqueness theorem of the semilinear equations is proved.

关 键 词：非线性伪抛物型方程 同胚 存在唯一性 

分 类 号：O175..8[理学—数学]