On the global solvability in Gevrey classes on the \(n\)-dimensional torus
The authors study global solvability in Gevrey classes on the \(n\)-dimensional torus \(\mathbb{T}^n\). A general necessary condition is first proved, similar to that in \textit{A. Corli} [Commun. Partial Differ. Equations 14, No. 1, 1--25 (1989; Zbl 0668.35002)] concerning the local case. Applications are then given to operators in \(\mathbb{T}^{n+1}\) of the form \[ P=- \partial^2_t- \biggl(\sum^n_{j=1} a_j(t)\,\partial_{x_j}\biggr)^2, \] where the functions \(a_j\) belong to \(G^s(\mathbb{T})\), \(s\geq 1\), and are real-valued.
scientific article; zbMATH DE number 2107214
scientific article