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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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A trajectory map for the pressureless Euler equations
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by Ryan Hynd PDF
Trans. Amer. Math. Soc. 373 (2020), 6777-6815 Request permission

Abstract:

We consider the dynamics of a collection of particles that interact pairwise and are restricted to move along the real line. Moreover, we focus on the situation in which particles undergo perfectly inelastic collisions when they collide. The equations of motion are a pair of partial differential equations for the particles’ mass distribution and local velocity. We show that solutions of this system exist for given initial conditions by rephrasing these equations in Lagrangian coordinates and then by solving for the associated trajectory map.
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Additional Information
  • Ryan Hynd
  • Affiliation: Department of Mathematics, University of Pennsylvania, 209 South 33rd Street, Philadelphia, Pennsylvania 19104
  • MR Author ID: 789875
  • Received by editor(s): February 28, 2019
  • Published electronically: July 28, 2020
  • © Copyright 2020 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 373 (2020), 6777-6815
  • MSC (2010): Primary 60B10, 35L04, and, 35Q85
  • DOI: https://doi.org/10.1090/tran/8118
  • MathSciNet review: 4155191