The blow-up rate for a non-scaling invariant semilinear wave equations in higher dimensions

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.