publication . Article . Other literature type . Preprint . 2018

Solutions to aggregation–diffusion equations with nonlinear mobility constructed via a deterministic particle approximation

SIMONE FAGIOLI;
Open Access
  • Published: 24 Aug 2018 Journal: Mathematical Models and Methods in Applied Sciences, volume 28, pages 1,801-1,829 (issn: 0218-2025, eissn: 1793-6314, Copyright policy)
  • Publisher: World Scientific Pub Co Pte Lt
Abstract
<jats:p> We investigate the existence of weak type solutions for a class of aggregation–diffusion PDEs with nonlinear mobility obtained as large particle limit of a suitable nonlocal version of the follow-the-leader scheme, which is interpreted as the discrete Lagrangian approximation of the target continuity equation. We restrict the analysis to bounded, non-negative initial data with bounded variation and away from vacuum, supported in a closed interval with zero-velocity boundary conditions. The main novelties of this work concern the presence of a nonlinear mobility term and the non-strict monotonicity of the diffusion function. As a consequence, our result ...
Subjects
free text keywords: Modelling and Simulation, Applied Mathematics, Mathematics - Analysis of PDEs
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