常微分不等式及其在半线性波动方程的应用

Abstract

Abstract:

In this paper, we first derive some blow-up results for two ordinary differential inequalities with variable coefficients, which are the generalizations of Theorem 3.1 in Li and Zhou^[3]. Second, as an application of the improved ordinary differential inequality, we consider the Cauchy problem for the semilinear wave equation with scale-invariant damping and deduce the upper bound of the lifespan for the case $\mu>1$ and $ 1 < p < 1+\frac{2}{n}$ under some suitable assumptions for the initial data. The method for the latter result is due to Lai and Zhou^[11].

Key words: Ordinary differential inequality, Semilinear wave equation, Lifespan

CLC Number:

O175.2

Shoujun Huang,Xiwang Meng. Improved Ordinary Differential Inequality and Its Application to Semilinear Wave Equations[J].Acta mathematica scientia,Series A, 2020, 40(5): 1319-1332.

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References 19

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Improved Ordinary Differential Inequality and Its Application to Semilinear Wave Equations

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