Publications
Last modified Mar 28 2024.

Articles in refereed international journals

  1. J.C. Miranda, A. J. Arenas, G. Gonzalez-Parra and L. M. Villada. Existence of Traveling Waves of a Diffusive Susceptible–Infected–Symptomatic–Recovered Epidemic Model with Temporal Delay . Mathematics, 12 (5), 710 (2024),
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  2. F. A. Chiarello, H. D. Contreras and L. M. Villada. Existence of entropy weak solutions for 1D non-local traffic models with space-discontinous flux . J. Eng. Math., 141 (9), (2023),
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  3. R. Bürger, H. D. Contreras and L. M. Villada. A Hilliges-Weidlich-type scheme for a one-dimensional scalar conservation law with nonlocal flux. Netw. Heterog. Media, 18 , (2023), pp 664-693.
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  4. P. Amorim, R. Bürger, R. Ordoñez and L. M. Villada. Global existence in a food chain model consisting of two competitive preys, one predator and chemotaxis. Nonlin. Anal. Real World Appl, 69 , 103703, (2023).
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  5. F. A. Chiarello, H. D. Contreras and L. M. Villada. Nonlocal reaction traffic flow model with on-off ramps. Netw. Heterog. Media, 17 (2), (2022) pp. 203-226 .
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  6. R. Bürger, C. Chalons, R. Ordoñez and L. M. Villada. A multiclass Lighthill-Whitham-Richards traffic model with a discontinuous velocity function . Netw. Heterog. Media, 16 (2), (2021) pp. 187-219.
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  7. R. Bürger, E. Gavilan, D. Inzunza, P. Mulet and L.M. Villada. Exploring a convection-diffusion-reaction model of the propagation of forest fires: computation of risk maps for heterogeneous environments. Mathematics, 8 (10), 1674 (2020).
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  8. R. Bürger, P. Goatin, D. Inzunza, and L.M. Villada. A non-local pedestrian flow model accounting for anisotropic interactions and domain boundaries Math. Biosci. Eng., 17 (5), (2020) pp. 5883-5906.
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  9. R. Bürger, E. Gavilan, D. Inzunza, P. Mulet and L.M. Villada. Implicit-explicit methods for a convection-diffusion-reaction model of the propagation of forest fires. Mathematics, 8 (6), 1034 (2020).
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  10. R. Bürger, R. Ordoñez, M. Sepúlveda and L. M. Villada. Numerical analysis of a three-species chemotaxis model. Comput. Math. Appl., 80 (1), (2020), pp. 183-203.
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  11. F. A. Chiarello, P. Goatin and L. M. Villada. Lagrangian-antidiffusive remap schemes for non-local multi-class traffic flow models. Comput. Appl. Math., 39 (2), 60 (2020).
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  12. P. Amorim, B. Telch and L. M. Villada A reaction-diffusion predator-prey model with pursuit, evasion, and nonlocal sensing. Math. Biosci. Eng., 16 (2019), pp. 5114-5145.
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  13. R. Bürger, D. Inzunza, P. Mulet and L.M. Villada. Implicit-explicit methods for a class of nonlinear nonlocal gradient flow equations modelling collective behaviour. Appl. Numer. Math., 144 (2019), pp. 234-252.
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  14. R. Bürger, D. Inzunza, P. Mulet and L.M. Villada. Implicit-explicit schemes for nonlinear nonlocal equations with a gradient flow structure in one space dimension. Numer. Meth. Partial Diff. Eqns., 35 (2019), pp. 1008-1034.
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  15. R. Bürger, G. Chowell, E. Gavilan, P. Mulet and L.M. Villada. Numerical solution of a spatio-temporal predator-prey model with infected prey. Math. Biosci. Eng. , 16 (2019), pp. 438-473.
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  16. C. Chalons, P. Goatin and L.M.Villada. High order numerical schemes for one-dimension non-local conservation laws. SIAM J. Sci. Comput., 40 (2018), pp. A288-A305.
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  17. R. Bürger, G. Chowell, E. Gavilan, P. Mulet and L.M. Villada. Numerical solution of a spatio-temporal gender-structured model for hantavirus infection in rodents Math. Biosci. Eng., 15 (2018), pp. 95-123.
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  18. R. Bürger, C. Chalons and L.M. Villada. Lagrangian-Remap schemes for models of polydisperse sedimentation. Numer. Meth. Partial Diff. Eqns. , 32 (2016), pp. 1109-1136.
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  19. S. Boscarino, R. Bürger, P. Mulet, G. Russo and L.M. Villada. On linearly implicit imex Runge-Kutta methods for degenerate convection-diffusion problems modeling polydisperse sedimentation. Bull. Braz. Math. Soc. (N.S.), 47 (2016), pp. 171-185.
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  20. R. Bürger, C. Chalons and L.M. Villada. On second-order antidiffusive Lagrangian-Remap schemes multispecies kinematic flow models. Bull. Braz. Math. Soc. (N.S.), 47 (2016), pp. 187-200.
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  21. R. Bürger, G. Chowell, P. Mulet and L.M. Villada. Modelling the spatial-temporal progression of the 2009 A/H1N1 influenza pandemic in Chile. Math. Biosci. Eng., 13 (2016), pp. 43-65.
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  22. S. Boscarino, R. Bürger, P. Mulet, G. Russo and L.M. Villada. Linearly implicit IMEX Runge-Kutta methods for a class of degenerate convection-diffusion problems. SIAM J. Sci. Comput., 37 (2015), pp. B305-B331.
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  23. R. Bürger, C. Chalons and L.M. Villada. Anti-diffusive and random-sampling Lagrangian-remap schemes for the multiclass Lighthill-Whitham-Richards traffic model. SIAM J. Sci. Comput., 35 (2013), pp. B1341-B1368.
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  24. R. Bürger, P. Mulet and L.M. Villada. Regularized nonlinear solvers for IMEX methods applied to diffusively corrected multi-species kinematic flow models. SIAM J. Sci. Comput., 35 (2013), pp. B751-B777.
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  25. R. Bürger, P. Mulet and L.M. Villada. A diffusively corrected multiclass Lighthill-Whitham-Richards traffic model with anticipation lengths and reaction times. Adv. Appl. Math. Mech., 5 (2013), pp. 728-758.
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  26. R. Bürger, P. Mulet and L.M. Villada. Spectral WENO schemes with Adaptive Mesh Refinement for models of polydisperse sedimentation. ZAMM Z. Angew. Math. Mech., 93 (2013), pp. 373-386.
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Submitted

  • H. D. Contreras, P. Goatin and L. M. Villada. A two-lane bidirectional nonlocal traffic model (Preprint)

  • R. Bürger, Y. Martinez and L. M. Villada. Front tracking and parameter identification for a conservation law with a space-dependent coefficient modeling granular segregatio (Preprint)

  • P. Goatin, D. Inzunza and L. M. Villada. Nonlocal macroscopic models os multi-population pedestrian flows for walking facilities optimization (Preprint)

  • M. Sepulveda, N. Torres and L. M. Villada. Well-posedness and numerical analysis of an elapsed time model with strongly coupled neural networks (Preprint)

    • Proceedings

    1. A. Würth , P. Goatin and L. M. VIllada , A cheap and easy-to-implement upwind scheme for second order traffic flow models . (preprint) Proceedings of Hyperbolic Problems: Theory, Numerics and Applications. to appear.

    2. D. Inzunza, P. Goatin and L. M. Villada. Numerical comparison of nonlocal macroscopic models of multi-population pedestrian flows with anisotropic kernel . (preprint) Proceedings of Hyperbolic Problems: Theory, Numerics and Applications. to appear.

    3. F. A. Chiarello, P. Goatin and L. M. Villada.
      High-order Finite Volume WENO schemes for non-local multi-class traffic flow models.
      In: Alberto Bressan, Marta Lewicka, Dehua Wang, Yuxi Zheng (eds.), Hyperbolic Problems: Theory, Numerics and Applications. AIMS Series on Applied Mathematics vol. 10 American Institute of Applied Mathematics, Springfield, MO, USA, pp. 353-360, (2020).
      (Journal page)

    4. R. Bürger, P. Mulet and L.M. Villada.
      Adaptive Mesh Refinement for spectral WENO schemes for efficient simulation of polydisperse sedimentation processes.
      In: F. Ancona, A. Bressan, P. Marcati and A. Marson (eds.), Hyperbolic Problems: Theory, Numerics and Applications. AIMS Series on Applied Mathematics vol. 8 American Institute of Applied Mathematics, Springfield, MO, USA, pp. 381-388, (2014)
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    5. H. A. Escorcia, L. M. Villada, M. F. Toro y C. E. Mejía.
      Uso de un software como propuesta metodológica para la enseñanza de ecuaciones diferenciales
      Lecturas Matemáticas. Vol Especial (27) (2006), pp. 361-369.
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