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NONLOCAL CROSS-INTERACTION SYSTEMS ON GRAPHS: NONQUADRATIC FINSLERIAN STRUCTURE AND NONLINEAR MOBILITIES.
- Source :
-
SIAM Journal on Mathematical Analysis . 2023, Vol. 55 Issue 6, p7039-7076. 38p. - Publication Year :
- 2023
-
Abstract
- We study the evolution of a system of two species with nonlinear mobility and nonlocal interactions on a graph whose vertices are given by an arbitrary, positive measure. To this end, we extend a recently introduced 2-Wasserstein-type quasi-metric on generalized graphs, which is based on an upwind-interpolation, to the case of two-species systems; concave, nonlinear mobilities; and p \not= 2. We provide a rigorous interpretation of the interaction system as a gradient flow in the Finslerian setting, arising from the new quasi-metric. [ABSTRACT FROM AUTHOR]
- Subjects :
- *NONLINEAR integral equations
Subjects
Details
- Language :
- English
- ISSN :
- 00361410
- Volume :
- 55
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- SIAM Journal on Mathematical Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 174808644
- Full Text :
- https://doi.org/10.1137/22M1470955