论文标题
在有界域中具有非线性记忆项的分数扩散波方程的关键指数上
On the critical exponents for a fractional diffusion-wave equation with a nonlinear memory term in a bounded domain
论文作者
论文摘要
在本文中，我们证明了一个时间分数扩散波方程的尖锐爆炸和全局存在结果，在有界域中具有非线性记忆项，其中时间是caputo类型的时间。此外，我们还为在有界域中具有非线性内存项的波动方程不存在的全局解决方案不存在。爆炸结果证明是基于征函数方法和用于普通分数差异不平等的溶液的渐近性能。
In this paper, we prove sharp blow-up and global existence results for a time fractional diffusion-wave equation with a nonlinear memory term in a bounded domain, where the fractional derivative in time is taken in the sense of Caputo type. Moreover, we also give a result for nonexistence of global solutions to a wave equation with a nonlinear memory term in a bounded domain. The proof of blow-up results is based on the eigenfunction method and the asymptotic properties of solutions for an ordinary fractional differential inequality.
