Lagrangian flows and the one-dimensional Peano phenomenon for ODEs

Crippa, Gianluca. (2011) Lagrangian flows and the one-dimensional Peano phenomenon for ODEs. Journal of Differential Equations, 250 (7). pp. 3135-3149.

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Official URL: http://edoc.unibas.ch/47271/

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We consider the one-dimensional ordinary differential equation with a vector field which is merely continuous and nonnegative, and satisfies a condition on the amount of zeros. Although it is classically known that this problem lacks uniqueness of classical trajectories, we show that there is uniqueness for the so-called regular Lagrangian flow (by now usual notion of flow in nonsmooth situations), as well as uniqueness of distributional solutions for the associated continuity equation. The proof relies on a space reparametrization argument around the zeros of the vector field.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Analysis (Crippa)
UniBasel Contributors:Crippa, Gianluca
Item Type:Article, refereed
Article Subtype:Research Article
Note:Publication type according to Uni Basel Research Database: Journal article
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Last Modified:30 Nov 2017 07:35
Deposited On:30 Nov 2017 07:35

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