Freezing in space-time: a functional equation linked with a PDE system

Burdzy, Krzysztof and Ostaszewski, Adam ORCID: 0000-0003-2630-8663 (2023) Freezing in space-time: a functional equation linked with a PDE system. Journal of Mathematical Analysis and Applications, 524 (2). ISSN 0022-247X

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Abstract

We analyze the functional equation F (x+F (x)) = −F (x) and reveal its relationship with a system of partial differential equations arising as the hydrodynamic limit of a system of pinned billiard balls on the line. The system of balls must freeze at some time, i.e., no velocity may change after the freezing time. The terminal velocity and the freezing time profiles play the role of boundary conditions for the PDEs (qua terminal conditions, despite being “initial conditions” from the wave equation perspective pursued here). Solutions to the functional equation provide the link between the freezing time and terminal velocity profiles on the one hand, and the solution to the PDE in the entirety of the space-time domain on the other.

Item Type:	Article
Official URL:	https://www.sciencedirect.com/journal/journal-of-m...
Additional Information:	© 2023 Elsevier Inc.
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	10 Jan 2023 10:33
Last Modified:	04 Nov 2024 08:00
URI:	http://eprints.lse.ac.uk/id/eprint/117826

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