Methods and Applications of Analysis

Volume 30 (2023)

Number 4

Sticky particles with sticky boundary

Pages: 129 – 148

DOI: https://dx.doi.org/10.4310/MAA.2023.v30.n4.a1

Author

Adrian Tudorascu (School of Mathematical and Data Sciences, West Virginia University, Morgantown, WV, USA)

Abstract

We study the pressureless Euler system in an arbitrary closed subset of the real line. We show that the no-slip/sticky boundary condition is natural and yields a well-posed problem which is treated by means of sticky particles solutions, Lagrangian solutions to the Cauchy problem and an appropriate (and natural) reflection principle.

Keywords

pressureless Euler, sticky particles system, sticky particles flow equation, scalar conservation laws, Lagrangian coordinates

2010 Mathematics Subject Classification

35A02, 35C99, 35F50, 35Q70, 35R06

Full Text (PDF format)

Received 3 October 2022

Accepted 19 July 2024

Published 7 August 2024