The Cauchy problem for $p$-evolution equations with initial data in Gelfand-Shilov spaces

Abstract

We study the Cauchy problem for a class of linear evolution equations of arbitrary order with coefficients depending both on time and space variables. Under suitable decay assumptions on the coefficients of the lower order terms for $|x|$ large, we prove a well-posedness result in Gelfand-Shilov spaces.

27 pages