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Nonexistence of global solutions for a class of complex vector fields on two-torus. (English) Zbl 1173.35406
Summary: The goal of this paper is study the global solvability of a class of complex vector fields of the special form L \(= \partial / \partial t + (a+ib)(x)\partial / \partial x , a,b \in C^\infty (S^1; \mathbb R)\), defined on two-torus \(\mathbb T^2 \cong \mathbb R^2 / 2\pi \mathbb Z^2\). The kernel of transpose operator \(^t\)L is described and the solvability near the characteristic set is also studied.

MSC:
35F10 Initial value problems for linear first-order PDEs
35A21 Singularity in context of PDEs
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