Asymptotic analysis for a pseudo-parabolic equation with nonstandard growth conditions. Issue 13 (2nd September 2022)

• Record Type: Journal Article
• Authors: Qu, Chengyuan; Zhou, Wenshu
• Is Part Of: Applicable analysis. Volume 101:Issue 13(2022)
• Page Start: 4701
• Page End: 4720
• Publication Date: 2022-09-02
• Subjects: X. Zou; Pseudo-parabolic equation -- nonstandard growth conditions -- potential well method -- asymptotic behavior; Primary 35K58 -- 35K35 -- 35B40; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2020.1869941
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : The main goal of this work is to study a semilinear pseudo-parabolic equation with nonstandard growth conditions. For initial energy J ( u 0 ) ≤ d, by using the generalized potential well method, we establish a sharp threshold result on global existence or blow-up weak solution. On the other hand, we also show the asymptotic behavior of solutions and the blow-up time estimates. The optimal estimations: the asymptotic behavior are obtained when the blow-up occurs. Moreover, for high initial energy J ( u 0 ) > d, we illustrate the conditions on global existence or blow-up.