We consider in this article the damped wave equation in the scale-invariant case with combined two nonlinearities as source term, namely ${\left|u_t\right|}^p+{\left|u\right|}^q$, and with small initial data. Owing to a better understanding of the influence of the damping term ($\frac{\mu }{1+t}{u}_t$) in the global dynamics of the solution, we obtain a new interval for $\mu$ that we conjecture to be closer to optimality, or probably optimal, and, thus, characterizes the threshold between the blow-up and the global existence regions. Moreover, taking advantage of the techniques employed in the problem with mixed nonlinearities, we prove for the damped wave equation with only one nonlinearity term ${\left|u_t\right|}^p$ that the blow-up region is now given by $p\in (1,p_G(N+\mu )]$ where $p_G\left(N\right)$ is the Glassey exponent. We think that this new interval for $\mu$ has better chances to characterize the threshold in this case.

在本文中，我们考虑了比例不变情况下的阻尼波方程，其中结合了两个非线性作为源项，即${\left|{ü}_{Ť}\right|}^p+{\left|ü\right|}^q$，且初始数据较少。由于更好地理解了阻尼项的影响（$\frac{\mu }{\mathrm{1个}+Ť}{ü}_{Ť}$）在解决方案的整体动力学中，我们获得了一个新的区间 $\mu$我们猜想是更接近于最优，或者可能是最优，因此表征了爆炸与全局存在区域之间的阈值。此外，利用混合非线性问题中使用的技术，我们证明了只有一个非线性项的阻尼波方程${\left|{ü}_{Ť}\right|}^p$ 爆炸区域现在由 $p\in （\mathrm{1个}，p_G（ñ+\mu ）]$ 哪里 $p_G（ñ）$是Glassey指数。我们认为，$\mu$ 在这种情况下，更有机会描述阈值。