华南师范大学学报(自然科学版)
華南師範大學學報(自然科學版)
화남사범대학학보(자연과학판)
JOURNAL OF SOUTH CHINA NORMAL UNIVERSITY (NATURAL SCIENCE EDITION)
2014年
3期
30-33
,共4页
变指数%非线性拟抛物方程%弱解%渐近行为%支集
變指數%非線性擬拋物方程%弱解%漸近行為%支集
변지수%비선성의포물방정%약해%점근행위%지집
variable exponent%nonlinear pseudoparabolic equation%weak solution%asymptotic behavior%support
关注一类具变指数非线性拟抛物方程初边值问题弱解的渐近行为和弱解支集的单调性问题。利用泛函的凸性,得到弱解的能量等式,根据此结果并使用 Poincaré不等式和 H?lder 不等式,讨论了具变指数非线性拟抛物方程弱解的渐近行为。此外,使用 Steklov 均值性质,导出弱解的比较原理,在一维情形中,利用该比较原理,证明了此拟抛物方程弱解支集的单调性。
關註一類具變指數非線性擬拋物方程初邊值問題弱解的漸近行為和弱解支集的單調性問題。利用汎函的凸性,得到弱解的能量等式,根據此結果併使用 Poincaré不等式和 H?lder 不等式,討論瞭具變指數非線性擬拋物方程弱解的漸近行為。此外,使用 Steklov 均值性質,導齣弱解的比較原理,在一維情形中,利用該比較原理,證明瞭此擬拋物方程弱解支集的單調性。
관주일류구변지수비선성의포물방정초변치문제약해적점근행위화약해지집적단조성문제。이용범함적철성,득도약해적능량등식,근거차결과병사용 Poincaré불등식화 H?lder 불등식,토론료구변지수비선성의포물방정약해적점근행위。차외,사용 Steklov 균치성질,도출약해적비교원리,재일유정형중,이용해비교원리,증명료차의포물방정약해지집적단조성。
The asymptotic behavior and monotonicity support of weak solutions to the initial-boundary value problem for a class of nonlinear pseudoparabolic equation with variable exponent are considered. The energy equality of weak solutions is obtained by using convexity of functional. By this and Poincaré's and Hlder's inequalities the as-ymptotic behavior of weak solutions to the nonlinear pseudoparabolic equation with variable exponent is discussed. The comparison principle is obtained by using of Steklov mean property of weak solutions. By this comparison prin-ciple,the monotonicity support of weak solutions is proved in 1-dimension.