论文标题
分数波方程系统的全球存在和解决方案的爆炸
Global existence and blow-up of solutions for a system of fractional wave equations
论文作者
论文摘要
我们研究了一个弱耦合的半线性分数波方程的2x2系统的Cauchy问题，其中具有R+ X RN中的多项式非线性。在指数的适当条件下，时间衍生物的分数顺序，表明存在尺寸n的阈值n，为此，小型数据全球溶液以及有限的时间爆破解决方案存在。此外，我们研究了全球解决方案的L1-DECAY估计值。
We investigate the Cauchy problem for a 2x2-system of weakly coupled semi-linear fractional wave equations with polynomial nonlinearities posed in R+ x RN. Under appropriate conditions on the exponents and the fractional orders of the time derivatives, it is shown that there exists a threshold value of the dimension N, for which, small data-global solutions as well as finite time blowing-up solutions exist. Furthermore, we investigate the L1-decay estimates of global solutions.
