论文标题
Cauchy问题，$ 3 $ - 进化方程，带有Gelfand-Shilov空间中的数据
The Cauchy problem for $3$-evolution equations with data in Gelfand-Shilov spaces
论文作者
论文摘要
我们认为，$ 3 $进化的运营商$ P $（t，x）$的Cauchy问题 - 取决于系数和复杂的有价值的下订单条款。我们假设初始数据是常规的，并承认无穷大的指数衰减，也就是说，该数据属于某些类型$ \ Mathscr {S} $的Gelfand-Shilov空间。在$ p $系数的虚构部分的衰减的适当假设下，我们证明存在具有相同gevrey juardiality的解决方案，我们描述了其$ | x |的行为\ to \ infty $。
We consider the Cauchy problem for a $3$-evolution operator $P$ with $(t,x)$-depending coefficients and complex valued lower order terms. We assume the initial data to be Gevrey regular and to admit an exponential decay at infinity, that is, the data belong to some Gelfand-Shilov spaces of type $\mathscr{S}$. Under suitable assumptions on the decay at infinity of the imaginary parts of the coefficients of $P$ we prove the existence of a solution with the same Gevrey regularity of the data and we describe its behavior for $|x| \to\infty$.
