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

Abstract

We consider the semilinear wave equation $${\partial }_t^{2}u-\Delta u=f(u),(x,t)\in {\mathbb{R}}^N\times [0,T),(1)$$ with $f(u)=|u{|}^{p-1}u{\log }^a(2+u^2)$, where $p>1$ and $a\in \mathbb{R}$, 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 \cite{HZjmaa2020}. Our goal here is to extend this result to higher dimensions.

arXiv commentarXiv admin note: substantial text overlap with arXiv:1906.12059

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Cited by in corpus (2)

• Universal estimates and Liouville theorems for superlinear problems without scale invariance
• The blow-up rate for a non-scaling invariant semilinear heat equation