The blow-up rate for a non-scaling invariant semilinear wave equations in higher dimensions. (November 2021)

• Record Type: Journal Article
• Authors: Hamza, Mohamed Ali; Zaag, Hatem
• Is Part Of: Nonlinear analysis. Volume 212(2021)
• Publication Date: 2021-11
• Subjects: 35L05 -- 35B44 -- 35L71 -- 35L67 -- 35B40; Semilinear wave equation -- Blow-up -- Non scaling invariance -- Higher dimensions; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2021.112445
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We consider the semilinear wave equation ∂ t 2 u − Δ u = f ( u ), ( x, t ) ∈ R N × [ 0, T ), ( 1 ) with f ( u ) = | u | p − 1 u log a ( 2 + u 2 ), where p > 1 and a ∈ R, with subconformal power nonlinearity. We will show that the blow-up rate of any singular solution of (1) is given by the ODE solution associated with ( 1 ), The result in one space dimension, has been proved in Hamza and Zaag (2020). Our goal here is to extend this result to higher dimensions.