PDEmas

PEOPLE

JOSÉ ALFREDO CAÑIZO RINCÓN

LINES OF RESEARCH

My research work deals mainly with mathematical models in Biology and Physics. This includes theory of integro-differential equations, especially kinetic equations, coagulation and fragmentation models, Boltzmann equations as well as nonlocal PDE in several contexts. I am interested in the analytic properties of these models, their asymptotic behaviour and their related mathematical techniques.

ARTICLES

  1. M. J. Cáceres, J. A. Cañizo, N. Torres. Comparison principles and asymptotic behavior of delayed age-structured neuron models. Preprint , 2025. Journal · arXiv
  2. R. Alonso, V. Bagland, J. A. Cañizo, B. Lods, S. Throm. One-dimensional inelastic Boltzmann equation: Stability and uniqueness of self-similar L1-profiles for moderately hard potentials. arXiv preprint arXiv:2408.04069, 2024. Journal · arXiv
  3. J. A. Cañizo, N. Tassi. A uniform-in-time nonlocal approximation of the standard Fokker-Planck equation. arXiv preprint arXiv:2407.03870, 2024. Journal · arXiv
  4. R. Alonso, V. Bagland, J. A. Cañizo, B. Lods, S. Throm. Relaxation in Sobolev spaces and L1 spectral gap of the 1D dissipative Boltzmann equation with Maxwell interactions. arXiv preprint arXiv:2407.01628, 2024. Journal · arXiv
  5. J. A. Cañizo, A. Ramos Lora. Discrete minimizers of the interaction energy in collective behavior: a brief numerical and analytic review. arXiv preprint arXiv:2403.00594, 2024. Journal · arXiv
  6. M. J. Cáceres, J. A. Cañizo, A. Ramos Lora. Sequence of pseudo-equilibria describes the long-time behaviour of the NNLIF model with large delay. Physical Review E. 110(6),064308, 2024. Journal · arXiv
  7. M. J. Cáceres, J. A. Cañizo, A. Ramos Lora. On the asymptotic behavior of the NNLIF neuron model for general connectivity strength.  To appear in Communications in Mathematical Physics, 2024. Journal · arXiv
  8. J. A. Cañizo, S. Mischler. Harris-type results on geometric and subgeometric convergence to equilibrium for stochastic semigroups. Journal of Functional Analysis 284 (7), 109830, 2023. Journal · arXiv
  9. R. J. Alonso, V. Bagland, J. A. Cañizo, B. Lods, S. Throm. One-dimensional inelastic Boltzmann equation: Regularity\& uniqueness of self-similar profiles for moderately hard potentials. arXiv preprint arXiv:2211.03446, 2022. Journal · arXiv
  10. J. A. Cañizo, G. López, J. Pérez. IMAG, the Institute of Mathematics of the University of Granada. European Mathematical Society Magazine, 34-37, 2022. Journal · arXiv
  11. José A. Cañizo and Sebastian Throm. The scaling hypothesis for Smoluchowski’s coagulation equation with bounded perturbations of the constant kernel. Journal of Differential Equations 270:285-342, 2021. Journal · arXiv
  12. José A. Cañizo, Pierre Gabriel and Havva Yoldaş. Spectral gap for the growth-fragmentation equation via Harris’s Theorem. SIAM J. Math. Anal. 53(5), 5185–5214, 2021. Journal · arXiv
  13. J. A. Cañizo, B. Lods, S. Throm. Contractivity for Smoluchowski’s coagulation equation with solvable kernels. Bulletin of the London Mathematical Society 53 (1), 248-258, 2021. Journal · arXiv
  14. J. A. Cañizo, C. Cao, J. Evans, H. Yoldaş. Hypocoercivity of linear kinetic equations via Harris’s Theorem. Kinetic and Related Models 13(1):97–128, 2019. Journal · arXiv
  15. José A. Cañizo, A. Einav, B. Lods. Uniform moment propagation for the Becker-Döring equations. Proceedings of the Royal Society of Edinburgh Section A: Mathematics 149 (4), 995-1015, 2019. Journal · arXiv
  16. J. A. Cañizo, J. A. Carrillo, M. Pájaro. Exponential equilibration of genetic circuits using entropy methods. Journal of Mathematical Biology 78 (1-2), 373-411, 2019. Journal · arXiv
  17. José A. Cañizo and Havva Yoldaş. Asymptotic behaviour of neuron population models structured by elapsed-time. Nonlinearity 32(2):464, 2019. Journal · arXiv
  18. J. A. Cañizo Rincón, A. Molino Salas. Improved energy methods for nonlocal diffusion problems. American Institute of Mathematical Sciences (AIMS), 2018. Journal · arXiv
  19. J. A. Cañizo, A. Einav, B. Lods. On the rate of convergence to equilibrium for the linear Boltzmann equation with soft potentials. Journal of Mathematical Analysis and Applications 462 (1), 801-839, 2018. Journal · arXiv
  20. José A. Cañizo and Francesco Patacchini. Discrete minimisers are close to continuum minimisers for the interaction energy. Calculus of Variations & PDE 57(24), 2018. Journal · arXiv
  21. M. J. Cáceres, J. A. Cañizo. Close-to-equilibrium behaviour of quadratic reaction–diffusion systems with detailed balance. Nonlinear Analysis 159, 62-84, 2017. Journal · arXiv
  22. José A. Cañizo, Amit Einav and Bertrand Lods. Trend to Equilibrium for the Becker-Döring Equations: An Analogue of Cercignani’s Conjecture. Analysis & PDE, 2017. Journal · arXiv
  23. J. A. Cañizo, B. Lods. Exponential trend to equilibrium for the inelastic Boltzmann equation driven by a particle bath. Nonlinearity 29 (5), 1687, 2016. Journal · arXiv
  24. J. A. Cañizo, J. A. Carrillo, P. Laurençot, J. Rosado. The Fokker–Planck equation for bosons in 2d: Well-posedness and asymptotic behavior. Nonlinear Analysis 137, 291-305, 2016. Journal · arXiv
  25. Alethea B. T. Barbaro, José A. Cañizo, José A. Carrillo and Pierre Degond. Phase transitions in a kinetic flocking model of Cucker-Smale type. Multiscale Modelling and Simulation 14(3):1063–1088, 2016. Journal · arXiv
  26. J. A. Cañizo, J. A. Carrillo and F. S. Patacchini. Existence of Compactly Supported Global Minimisers for the Interaction Energy. Archive for Rational Mechanics and Analysis 217(3):1197–1217, 2015. Journal · arXiv
  27. Marzia Bisi, José A. Cañizo and Bertrand Lods. Entropy dissipation estimates for the linear Boltzmann operator. Journal of Functional Analysis 269(4):1028–1069, 2015. Journal · arXiv
  28. J. A. Cañizo, L. Desvillettes and K. Fellner. Improved duality estimates and applications to reaction-diffusion equations. Communications in Partial Differential Equations Vol. 39, No. 6, pp. 1185-1204, 2014. Journal · arXiv
  29. D. Balagué, J. A. Cañizo and P. Gabriel. Fine asymptotics of profiles and relaxation to equilibrium for growth-fragmentation equations with variable drift rates. Kinetic and Related Models Vol. 6, No. 2, pp. 219-243, 2013. Journal · arXiv
  30. R. Alonso, J. A. Cañizo, I. Gamba, C. Mouhot. A new approach to the creation and propagation of exponential moments in the Boltzmann equation. Communications in Partial Differential Equations 38 (1), 155-169, 2013. Journal · arXiv
  31. B. Lods and J. A. Cañizo. Exponential convergence to equilibrium for subcritical solutions of the Becker-Döring equations. Journal of Differential Equations Vol. 255, No. 5, pp. 905-950, 2013. Journal · arXiv
  32. J. A. Cañizo, J. A. Carrillo and S. Cuadrado. Measure solutions for some models in population dynamics. Acta Applicandae Mathematicae Vol. 123, No. 1, pp. 141-156, February 2013. Journal · arXiv
  33. J. A. Cañizo, J. A. Carrillo, M. E. Schonbek. Decay rates for a class of diffusive-dominated interaction equations. Journal of Mathematical Analysis and Applications 389 (1), 541-557, 2012. Journal · arXiv
  34. M. Bisi, J. A. Cañizo, B. Lods. Uniqueness in the Weakly Inelastic Regime of the Equilibrium State to the Boltzmann Equation Driven by a Particle Bath. SIAM Journal on Mathematical Analysis 43, 2640, 2011. Journal · arXiv
  35. M. J. Cáceres, J. A. Cañizo and S. Mischler. Rate of convergence to an asymptotic profile for the self-similar fragmentation and growth-fragmentation equations. Journal de Mathémathiques Pures et Appliquées Vol. 96, No. 4, pp. 334-362, 2011. Journal · arXiv
  36. M. J. Cáceres, J. A. Cañizo, S. Mischler. Rate of convergence to self-similarity for the fragmentation equation in L^ 1 spaces. Communications in Applied and Industrial Mathematics 1 (2), pp.299-308, 2011. Journal · arXiv
  37. J. A. Cañizo, J. Carrillo and J. Rosado. A well-posedness theory in measures for some kinetic models of collective motion. Mathematical Models and Methods in Applied Sciences Vol. 21, No. 3, pp. 515-539, 2011. Journal · arXiv
  38. F. Bolley, J. A. Cañizo and J. Carrillo. Stochastic Mean-Field Limit: Non-Lipschitz Forces & Swarming. Mathematical Models and Methods in Applied Sciences Vol. 21, No. 11, pp. 2179-2210, 2011. Journal · arXiv
  39. J. Carrillo, J. A. Cañizo and F. Bolley. Mean-field limit for the stochastic Vicsek model. Applied Mathematics Letters 25 (3), 339, 2011. Journal · arXiv
  40. J. A. Cañizo, S. Mischler. Regularity, local behavior and partial uniqueness for self-similar profiles of Smoluchowski’s coagulation equation. Revista Matemática Iberoamericana 27 (3), 803-839, 2011. Journal · arXiv
  41. J. A. Cañizo, L. Desvillettes, K. Fellner. Regularity and mass conservation for discrete coagulation–fragmentation equations with diffusion. Annales de l’IHP Analyse non linéaire 27 (2), 639-654, 2010. Journal · arXiv
  42. J. A. Cañizo, S. Mischler, C. Mouhot. Rate of convergence to self-similarity for Smoluchowski’s coagulation equation with constant coefficients. SIAM journal on mathematical analysis 41 (6), 2283-2314, 2010. Journal · arXiv
  43. J. A. Cañizo, L. Desvillettes, K. Fellner. Absence of gelation for models of coagulation-fragmentation with degenerate diffusion. Il Nuovo cimento della Società italiana di fisica 33 (1), 79, 2010. Journal · arXiv
  44. J. A. Cañizo, J. A. Carrillo, J. Rosado. Collective behavior of animals: Swarming and complex patterns. Arbor 186 (1035-1049), 1 46, 2010. Journal · arXiv
  45. J. A. Cañizo. Convergence to equilibrium for the discrete coagulation-fragmentation equations with detailed balance. Journal of Statistical Physics 129, 1-26, 2007. Journal · arXiv
  46. J. A. Cañizo. Some problems related to the study of interaction kernels: coagulation, fragmentation and diffusion in kinetic and quantum equations. Universidad de Granada, 2006. Journal · arXiv
  47. J. A. Cañizo. Asymptotic behavior of the generalized Becker-Döring equations for general initial data. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 461 (2064), 3731-3745, 2005. Journal · arXiv
  48. J. A. Cañizo, J. L. López, J. Nieto. Global L1 theory and regularity for the 3D nonlinear Wigner–Poisson–Fokker–Planck system. Journal of Differential Equations 198 (2), 356-373, 2004. Journal · arXiv
  49. J. C. Neu, J. A. Cañizo, L. L. Bonilla. Three eras of micellization. Physical Review E 66 (6), 061406 48, 2002. Journal · arXiv

PARTICIPATION IN CONFERENCES

These are the most recent conferences i have participated in during the last 10 years:

  1. Interactions between partial differential equations & functional inequalities. Seminar at the Mittag-Leffler Institute, November 22, 2016, Stockholm, Sweden.
  2. Asymptotic behaviour of the Becker-Döring equations. The 11th AIMS Conference on Dynamical Systems, Differential Equations and Applications, 1–5 July 2016, Orlando, Florida, USA.
  3. Recent advances on the theory of the Becker-Döring equations. Two-hour minicourse, 8th Summer School on Methods & Models in Kinetic Theory, 5–11 June 2016, Porto Ercole, Italy.
  4. Plenary speaker, Congreso Español de Jóvenes Investigadores. September 2015.
  5. Entropy dissipation inequalities for the linear Boltzmann equation. Entropy Methods, PDEs, Functional Inequalities, and Applications. 29 June – 4 July 2014, Banff, Canada.
  6. Asymptotic behavior for the Becker-Döring equations. Classical and Quantum Mechanical Models of Many-Particle Systems. 1 – 7 December 2013, Oberwolfach, Germany.
  7. Asymptotic behavior for the aggregation-diffusion equations. Young Researchers Workshop: Kinetic and Macroscopic Models for Complex Systems. 14 – 18 October 2013, College Park, Maryland, USA.