具有时变阻尼和幂型非线性的波动方程寿命和爆破率的估计

IF 0.7 4区数学 Q2 MATHEMATICS Funkcialaj Ekvacioj-Serio Internacia Pub Date : 2016-09-05 DOI:10.1619/fesi.62.157

K. Fujiwara, M. Ikeda, Yuta Wakasugi

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引用次数: 28

摘要

研究了具有时变阻尼的半线性波动方程Cauchy问题解的爆破行为。当阻尼有效且非线性为亚临界时，我们给出了爆破率和解的尖锐寿命估计。上估计由一个ODE参数证明，下估计由一种缩放变量的方法给出。

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Estimates of Lifespan and Blow-up Rates for the Wave Equation with a Time-dependent Damping and a Power-type Nonlinearity

We study blow-up behavior of solutions for the Cauchy problem of the semilinear wave equation with time-dependent damping. When the damping is effective, and the nonlinearity is subcritical, we show the blow-up rates and the sharp lifespan estimates of solutions. Upper estimates are proved by an ODE argument, and lower estimates are given by a method of scaling variables.

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