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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.

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