Publications
Last modified Nov 12 2024.

Articles in refereed international journals

  1. H. D. Contreras, P. Goatin and L. M. Villada. A two-lane bidirectional nonlocal traffic model J. Math Anal. Appl. 543 (2) , 129027 (2025)
    (Journal page) (Preprint)

  2. R. Bürger, Y. Martinez and L. M. Villada. Front tracking and parameter identification for a conservation law with a space-dependent coefficient modeling granular segregation Adv. Appl. Math. Mech. to appear (Preprint)

  3. 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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  4. 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),
    (Journal page)

  5. 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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  6. 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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  7. 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 .
    (Journal page)

  8. 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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  9. 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).
    (Journal page)

  10. 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.
    (Journal page)

  11. 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).
    (Journal page)

  12. 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.
    (Journal page)

  13. 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).
    (Journal page)

  14. 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.
    (Journal page)

  15. 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.
    (Journal page)

  16. 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.
    (Journal page)

  17. 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.
    (Journal page)

  18. 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.
    (Journal page)

  19. 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.
    (Journal page)

  20. 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.
    (Journal page)

  21. 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.
    (Journal page)

  22. 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.
    (Journal page)

  23. 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.
    (Journal page)

  24. 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.
    (Journal page)

  25. 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.
    (Journal page)

  26. 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.
    (Journal page)

  27. 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.
    (Journal page)

  28. 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.
    (Journal page)

Submitted

  • J. Barajas-Calonge, R. Bürger, P. Mulet and L. M. Villada. Invariant-region-preserving central WENO schemes for one-dimensional multispecies kinematic flow models (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 .
      In: Parés, C., Castro, M.J., Morales de Luna, T., Muñoz-Ruiz, M.L. (eds) Hyperbolic Problems: Theory, Numerics and Applications. Volume II . HYP 2022. SEMA SIMAI Springer Series, vol 35. Springer, Cham. pp 209-219. (2024)
      ( journal page )

    2. D. Inzunza, P. Goatin and L. M. Villada. Numerical comparison of nonlocal macroscopic models of multi-population pedestrian flows with anisotropic kernel .
      In: Parés, C., Castro, M.J., Morales de Luna, T., Muñoz-Ruiz, M.L. (eds) Hyperbolic Problems: Theory, Numerics and Applications. . Volume II HYP 2022. SEMA SIMAI Springer Series, vol 35. Springer, Cham. pp 371-381. (2024)
      ( journal page )

    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 , 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)
      (Journal page)

    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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