具阻尼振荡的半线性波动方程的临界指数
The critical exponent for semilinear wave equations with damped oscillations
AI总结：
该研究确定了一类带幂次非线性项且具特殊耗散的演化方程的全局小初值解的存在性指数，针对n=3的带黏弹性耗散的波动方程，相关爆破结果已被证明，且该指数最优。
AI中文摘要：
我们确定了一类演化方程在耗散效应下的全局小初值解的存在性指数，这类方程具有幂次非线性项，其耗散会衰减低频振荡并对高频产生过阻尼效应。对于带黏弹性耗散的波动方程，陈文辉近期证明了空间维数n=3时对应的爆破情况，表明该存在性指数是最优的。
英文摘要：
We determine the existence exponent for the global small data solutions for a class of evolution equations with power nonlinearity under the effect of a dissipation that dampen the oscillations at low frequencies and produce overdamping at high frequencies. In the case of the wave equation with viscoelastic dissipation, the counterpart of blow-up in space dimension $n=3$ has been very recently proved by Wenhui Chen, showing that the existence exponent is optimal.
