论文标题
具有量表不变的阻尼和时间导数非线性的弱耦合波方程的新爆炸结果
New blow-up result for the weakly coupled wave equations with a scale-invariant damping and time derivative nonlinearity
论文作者
论文摘要
我们在本文中考虑了\ textIt {scale-canvariant案例}中的波方程的弱耦合系统以及时间衍生的非线性。在通常的小初始数据假设下，我们通过获得临界曲线的新候选者来改善爆炸区域的划界。更确切地说，我们增强了在当前工作中考虑的系统中在\ cite {palmieri}中获得的结果。我们认为，我们的结果是最佳的，因为除了这里获得的爆破区域之外，我们可能会猜测解决方案的全球存在。
We consider in this article the weakly coupled system of wave equations in the \textit{scale-invariant case} and with time-derivative nonlinearities. Under the usual assumption of small initial data, we obtain an improvement of the delimitation of the blow-up region by obtaining a new candidate for the critical curve. More precisely, we enhance the results obtained in \cite{Palmieri} for the system under consideration in the present work. We believe that our result is optimal in the sense that beyond the blow-up region obtained here we may conjecture the global existence of the solution.
