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Journal Articles Communications on Pure and Applied Analysis Year : 2022

Well-posedness of an interaction model on Riemannian manifolds

Abstract

We investigate a model for collective behaviour with intrinsic interactions on smooth Riemannian manifolds. For regular interaction potentials, we establish the local well-posedness of measure-valued solutions defined via optimal mass transport. We also extend our result to the global well-posedness of solutions for manifolds with nonpositive bounded sectional curvature. The core concept underlying the proofs is that of Lipschitz continuous vector fields in the sense of parallel transport.
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Dates and versions

hal-03877707 , version 1 (06-12-2022)
hal-03877707 , version 2 (30-03-2023)

Licence

Attribution - NonCommercial - NoDerivatives

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Razvan C. Fetecau, Francesco S. Patacchini. Well-posedness of an interaction model on Riemannian manifolds. Communications on Pure and Applied Analysis, 2022, 21 (11), pp.3559-3585. ⟨10.3934/cpaa.2022114⟩. ⟨hal-03877707v2⟩

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