publication . Preprint . Article . Other literature type . 2018

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

Simone Fagioli; Emanuela Radici;
Open Access English
  • Published: 24 Aug 2018
<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 ...
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free text keywords: Mathematics - Analysis of PDEs, Modelling and Simulation, Applied Mathematics, Degenerate diffusion, Physics, Particle, Statistical physics, Weak type, Nonlinear system, Large particle
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