Global existence and blow-up for a mixed pseudo-parabolic p-Laplacian type equation with logarithmic nonlinearity-II. Issue 12 (10th September 2021)

• Record Type: Journal Article
• Authors: Ding, Hang; Zhou, Jun
• Is Part Of: Applicable analysis. Volume 100:Issue 12(2021)
• Page Start: 2641
• Page End: 2658
• Publication Date: 2021-09-10
• Subjects: Pseudo-parabolic equation -- p-Laplacian -- upper and lower bounds of blow-up time -- high initial energy; 35K70 -- 35B05 -- 35B40; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2019.1695784
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: This paper deals with the following mixed pseudo-parabolic p -Laplacian type equation with logarithmic nonlinearity 1 u t − Δ u t − d i v ( | ∇ u | p − 2 ∇ u ) = | u | q − 2 u log ⁡ | u | in a bounded domain with zero Dirichlet boundary condition, which was studied in our previous paper [J Math Anal Appl. 2019;478(2):393-420]. In view the results of [J Math Anal Appl. 2019;478(2):393-420], for the case (1) 1 < p ≤ q ≤ 2, i f n ≤ p, ≤ 2, i f 2 n n + 2 < p < n, < n p n − p, i f p ≤ 2 n n + 2, the global existence and blow-up results were got when J ( u 0 ) ≤ d, where d denotes the mountain-pass level. But for the case (2) 1 < p ≤ q a n d 2 < q < ∞, i f n ≤ p, n p n − p, i f 2 n n + 2 < p < n, the blow-up results were got when J ( u 0 ) ≤ M, where M ≤ d is a constant. In this paper, we extend and complete the results of [J Math Anal Appl. 2019;478(2):393-420] on the following three aspects: First, the blow-up results are got when J ( u 0 ) ≤ d and (2) are satisfied. Second, the upper and lower bounds of blow-up time are estimated. Third, the global existence and blow-up results are got when J ( u 0 ) > d .