摘要
考虑一类具变指数四阶抛物方程的初边值问题.利用Steklov均值、Hlder不等式和Young不等式,证明了弱解的唯一性;使用泛函的凸性,得到解的能量等式,利用此结果,讨论弱解的渐近行为.
An initial-boundary value problem for a class of fourth order parabolic equation with variable exponent is discussed. The uniqueness of weak solutions is proved by using the Steklov mean, Holderrs and Young＇s inequalities. The energy equality of weak solutions is obtained by using convexity of functional. By this the asymptotic behavior of weak solutions is discussed.
出处
《广西民族大学学报（自然科学版）》
CAS
2014年第4期41-45,共5页
Journal of Guangxi Minzu University ：Natural Science Edition
基金
国家自然科学基金(11371166)
关键词
变指数
四阶抛物方程
弱解
唯一性
渐近行为
variable exponent
fourth order parabolic equation
weak solution
uniqueness
asymptotic behavior
