Pressureless Euler alignment system with control

Giacomo Albi, Young Pil Choi, Axel Stefan Häck

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

We study a non-local hydrodynamic system with control. First, we characterize the control dynamics as a sub-optimal approximation to the optimal control problem constrained to the evolution of the pressureless Euler alignment system. We then discuss the critical thresholds that lead to global regularity or finite-time blow-up of strong solutions in one and two dimensions. Finally, we use a finite volume scheme, coupled with an implicit-explicit time integrator to solve numerically the stiff scale of the controlled system. Several numerical simulations are shown to validate the theoretical and computational results of the paper.

Original languageEnglish
Pages (from-to)1635-1664
Number of pages30
JournalMathematical Models and Methods in Applied Sciences
Volume28
Issue number9
DOIs
Publication statusPublished - 2018 Aug 1

Bibliographical note

Funding Information:
G. A. is supported by GNCS–INDAM fundings, and by the project “MIUR Departments of Excellence 2018-2022”. Y.-P. C. is supported by National Research Foundation of Korea (NRF) Grant funded by the Korea government (MSIP) (Nos. 2017R1C1B2012918 and 2017R1A4A1014735) and POSCO Science Fellowship of POSCO TJ Park Foundation. A.-S. H. acknowledges the support by DAAD–MIUR fundings.

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Applied Mathematics

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