论文标题
对半线性波方程的爆炸竞赛，具有比例不变的阻尼和非线性记忆项
A competition on blow-up for semilinear wave equations with scale-invariant damping and nonlinear memory term
论文作者
论文摘要
在本文中，我们调查了对半线性波方程解决方案的爆炸，并以$ \ mathbb {r}^n $中的比例不变性阻尼和非线性记忆项为单位，这可以由riemann-liouville-liouville分数的订单$ 1-γ$的集成$ 1-γ\ in（0,1）$表示。我们的主要兴趣是通过使用测试功能方法或广义的Kato型引理研究从阻尼项和记忆内核对非线性功能的爆破条件的混合影响。我们发现了一项新的竞争，尤其是在有效案例与无效案例之间的爆炸范围内，尤其是对于$γ$的小价值。
In this paper, we investigate blow-up of solutions to semilinear wave equations with scale-invariant damping and nonlinear memory term in $\mathbb{R}^n$, which can be represented by the Riemann-Liouville fractional integral of order $1-γ$ with $γ\in(0,1)$. Our main interest is to study mixed influence from damping term and the memory kernel on blow-up conditions for the power of nonlinearity, by using test function method or generalized Kato's type lemma. We find a new competition, particularly for the small value of $γ$, on the blow-up range between the effective case and the non-effective case.
