Singular properties of solutions for a parabolic equation with variable exponents and logarithmic source. (April 2022)

• Record Type: Journal Article
• Authors: Liu, Bingchen; Zhang, Min; Li, Fengjie
• Is Part Of: Nonlinear analysis. Volume 64(2022)
• Publication Date: 2022-04
• Subjects: Variable exponent -- Blow-up -- Extinction -- Global existence -- Initial energy; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2021.103449
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: This paper deals with a parabolic p ( x ) -Laplace equation with logarithmic source u q ( x ) log u . The singular properties of solutions are determined completely by classifying the initial energy. Moreover, we obtain a new extinction rate of solutions, where the order of the extinction rate is greater than the maximum of variable exponent q ( x ) . This kind of extinction rate could reflect the influence of logarithmic functions on the extinction of solutions more reasonably.