Asymptotic property of singular solutions in some nonstandard parabolic equation. (August 2021)

• Record Type: Journal Article
• Authors: Wang, Yuxi; Liu, Bingchen; Sun, Yurou
• Is Part Of: Nonlinear analysis. Volume 60(2021)
• Publication Date: 2021-08
• Subjects: p(x, t)-Laplacian -- Extinction rate -- Extinction time -- Blow-up rate -- Blow-up time; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2021.103301
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper, we study the asymptotic properties of singular solutions to some nonstandard parabolic equation involving p ( x, t ) -Laplacian and nonlocal anisotropic sources. First, we show the existence and uniqueness of weak solutions by using the Galerkin's approximations in the anisotropic Orlicz–Sobolev spaces. Second, in order to determine extinction rates and time of solutions, we prove some ordinary differential inequalities with the Sobolev embedding inequalities. Third, we combine priori estimates and the embedding theorems to show the rates and time estimates of blow-up solutions.