Blow-up and lifespan estimates for Nakao's type problem with nonlinearities of derivative type

Abstract

In the present paper, we investigate blow-up and lifespan estimates for a class of semilinear hyperbolic coupled system in ${\mathbb{R}}^n$ with $n⩾1$, which is part of the so-called Nakao's type problem weakly coupled a semilinear damped wave equation with a semilinear wave equation with nonlinearities of derivative type. By constructing two time-dependent functionals and employing an iteration method for unbounded multiplier with slicing procedure, the results of blow-up and upper bound estimates for the lifespan of energy solutions are derived. The model seems to be hyperbolic-like instead of parabolic-like. Particularly, the blow-up result for one dimensional case is optimal.

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Cited by in corpus (1)

• On the blow-up of solutions to semilinear damped wave equations with power nonlinearity in compact Lie groups