Nonlinear semigroups for nonlocal conservation laws

Mihály Kovács () and Mihály A. Vághy
Additional contact information
Mihály Kovács: Chalmers University of Technology and University of Gothenburg
Mihály A. Vághy: Pázmány Péter Catholic University

Partial Differential Equations and Applications, 2023, vol. 4, issue 4, 1-26

Abstract: Abstract We investigate a class of nonlocal conservation laws in several space dimensions, where the continuum average of weighted nonlocal interactions are considered over a finite horizon. We establish well-posedness for a broad class of flux functions and initial data via semigroup theory in Banach spaces and, in particular, via the celebrated Crandall–Liggett Theorem. We also show that the unique mild solution satisfies a Kružkov-type nonlocal entropy inequality. Similarly to the local case, we demonstrate an efficient way of proving various desirable qualitative properties of the unique solution.

Keywords: Nonlocal differential equation; Conservation law; Nonlinear semigroup; 35F25; 35Q49; 45K05 (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s42985-023-00249-9 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:pardea:v:4:y:2023:i:4:d:10.1007_s42985-023-00249-9

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/42985/

DOI: 10.1007/s42985-023-00249-9

Access Statistics for this article

Partial Differential Equations and Applications is currently edited by Zhitao Zhang

More articles in Partial Differential Equations and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().