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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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##### References:
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