Author:
Arias Junior Alexandre,Ascanelli Alessia,Cappiello Marco
Abstract
AbstractWe consider the Cauchy problem for a third-order evolution operator P with (t, x)-depending coefficients and complex-valued lower-order terms. We assume the initial data to be Gevrey regular with an exponential decay at infinity, that is, the data belong to some Gelfand–Shilov space of type $${\mathscr {S}}$$
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 $$|x| \rightarrow \infty $$
|
x
|
→
∞
.
Publisher
Springer Science and Business Media LLC
Subject
Mathematics (miscellaneous)
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