Solutions to aggregation-diffusion equations with nonlinear mobility constructed via a deterministic particle approximation
Abstract
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 nonnegative initial data in $L^{\infty} \cap BV$ away from vacuum and 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 applies also to strongly degenerate diffusion equations. The conclusions are complemented with some numerical simulations.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2018
- DOI:
- 10.48550/arXiv.1801.10114
- arXiv:
- arXiv:1801.10114
- Bibcode:
- 2018arXiv180110114F
- Keywords:
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- Mathematics - Analysis of PDEs