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Well-posedness for a transport equation with nonlocal velocity. (English) Zbl 1170.35004
The author in this paper studies a one-dimensional transport with nonlocal velocity, involving fractional powers of the minus Laplacian operator, which was considered by several authors early. He proofs some properties with weaker hypothesis.

35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35L60 First-order nonlinear hyperbolic equations
35L67 Shocks and singularities for hyperbolic equations
Full Text: DOI
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