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arXiv · 2005.01294

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

Wenhui Chen
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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 $n\geqslant 1$, 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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Wenhui Chen. 2020-05-04. Blow-up and lifespan estimates for Nakao's type problem with nonlinearities of derivative type. https://doi.org/10.1002/mma.8152

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