论文标题
对具有多个传播速度的广义三角形方程的弱耦合系统的小数据爆炸
Small data blow-up for the weakly coupled system of the generalized Tricomi equations with multiple propagation speeds
论文作者
论文摘要
在本文中，我们研究了具有多个传播速度的广义三角形方程的弱耦合系统的库奇问题。我们本文的目的是证明问题的数据爆炸结果很小，并且在Strauss类型的亚临界和关键案例中适当支持的问题的寿命估计值。证明是基于论文中论证的框架[17]。我们的新贡献之一是为自由方程式建造两个特殊解决方案的家族（参见（2.16）或（2.18），作为测试功能并证明了它们的多个属性。我们强调，本文中处理了两个具有两个不同传播速度的系统，并且对最初数据的假设从最初的数据中得到了提高，从而从积极的积极积极的效率上提高了积极性。
In the present paper, we study the Cauchy problem for the weakly coupled system of the generalized Tricomi equations with multiple propagation speeds. Our aim of this paper is to prove a small data blow-up result and an upper estimate of lifespan of the problem for a suitable compactly supported initial data in the subcritical and critical cases of the Strauss type. The proof is based on the framework of the argument in the paper [17]. One of our new contributions is to construct two families of special solutions to the free equation (see (2.16) or (2.18) as the test functions and prove their several properties. We emphasize that the system with two different propagation speeds is treated in this paper and the assumption on the initial data is improved from the point-wise positivity to the integral positivity.
