The sharp lifespan estimate for semilinear damped wave equation with Fujita critical power in high dimensions

Ning-An Lai; Yi Zhou

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arXiv · 1702.07073

The sharp lifespan estimate for semilinear damped wave equation with Fujita critical power in high dimensions

Ning-An Lai·Yi Zhou

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Abstract

This paper is concerned about the lifespan estimate to the Cauchy problem of semilinear damped wave equations with the Fujita critical exponent in high dimensions$(n\geq 4)$. We establish the sharp upper bound of the lifespan in the following form \begin{equation}\nonumber\\ \begin{aligned} T(\varepsilon)\leq \exp(C\varepsilon^{-\frac 2n}), \end{aligned} \end{equation} by using the heat kernel as the test function.

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Ning-An Lai, Yi Zhou. 2017-02-23. The sharp lifespan estimate for semilinear damped wave equation with Fujita critical power in high dimensions. https://arxiv.org/abs/1702.07073

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