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Solvability in the large for a class of complex vector fields on the cylinder. (English) Zbl 1235.35007
Summary: This work deals with global solvability of a class of complex vector fields of the form \(\mathcal L = \partial /\partial t + (a(x,t) + ib(x,t))\partial /\partial x\), where \(a\) and \(b\) are real-valued \(C^{\infty }\) functions, defined on the cylinder \(\varOmega = \mathbb R \times S^{1}\). Relatively compact (Sussmann) orbits are allowed. The connection with Malgrange’s notion of \(\mathcal L\)-convexity for supports is investigated.
MSC:
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35F05 Linear first-order PDEs
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