Lorenzo Liverani

2026

• Li Z., Liu K., Liverani L., Zuazua E.:
  Universal Approximation of Dynamical Systems by Semiautonomous Neural ODEs and Applications
  In: SIAM Journal on Numerical Analysis 64 (2026), p. 193 - 223
  ISSN: 0036-1429
  DOI: 10.1137/24M1679690
• Liverani L., Zuazua E.:
  HYCO: A formalism for Hybrid-Cooperative PDE modelling
  (2026)
• Liverani L., Zuazua E.:
  HYCO: Hybrid-Cooperative Learning for Data-Driven PDE Modeling
  (2026)
  URL: https://dcn.nat.fau.eu/wp-content/uploads/HYCO-LL-EZ.pdf
• Lopez Montero D., Liverani L., Zuazua E., Kobeleva X.:
  Hybrid Modeling of Whole-Brain Dynamics balances Data Fidelity and Interpretability
• Primio AD., Liverani L.:
  LARGE-TIME ASYMPTOTICS OF THE REGULARIZED MOORE-GIBSON-THOMPSON EQUATION WITH GURTIN-PIPKIN THERMAL LAW
  In: Discrete and Continuous Dynamical Systems. Series S (2026), p. 1-27
  ISSN: 1937-1632
  DOI: 10.3934/DCDSS.2026054
• Álvarez López A., Liverani L., Zuazua E.:
  Constructive interpolation and generalization rates for Neural ODEs: a control perspective

2025

• Crin-Barat T., Liverani L., Shou LY., Zuazua E.:
  Large-time asymptotics for hyperbolic systems with non-symmetric relaxation: An algorithmic approach
  In: Journal De Mathematiques Pures Et Appliquees 202 (2025), Article No.: 103757
  ISSN: 0021-7824
  DOI: 10.1016/j.matpur.2025.103757
• Dell'Oro F., Liverani L., Pata V., Quintanilla R.:
  Global attractors for Moore–Gibson–Thompson thermoelastic extensible beams and Berger plates
  In: Nonlinear Analysis-Real World Applications 84 (2025), Article No.: 104298
  ISSN: 1468-1218
  DOI: 10.1016/j.nonrwa.2024.104298
• Liverani L., Ognibene R., Felli V.:
  Quantitative spectral stability for the Neumann Laplacian in domains with small holes
  In: Journal of Functional Analysis (2025)
  ISSN: 0022-1236
  URL: https://www.sciencedirect.com/science/article/pii/S0022123624005056?via=ihub

2024

• Bazarra N., Fernández J.R., Liverani L., Quintanilla R.:
  Analysis of a thermoelastic problem with the Moore–Gibson–Thompson microtemperatures
  In: Journal of Computational and Applied Mathematics 438 (2024), Article No.: 115571
  ISSN: 0377-0427
  DOI: 10.1016/j.cam.2023.115571
• Liverani L., Pata V., Dell'Oro F., Quintanilla R.:
  On the Double Moore–Gibson–Thompson System of Thermoviscoelasticity
  In: Studies in Applied Mathematics (2024)
  ISSN: 0022-2526
  DOI: 10.1111/sapm.12784
  URL: https://onlinelibrary.wiley.com/doi/10.1111/sapm.12784

2023

• Antonietti PF., Liverani L., Pata V.:
  Lack of superstable trajectories in linear viscoelasticity: a numerical approach
  In: Numerische Mathematik 153 (2023), p. 611-633
  ISSN: 0029-599X
  DOI: 10.1007/s00211-023-01351-1
• Liverani L., Mammeri Y., Pata V., Quintanilla R.:
  On the linearized Whitham-Broer-Kaup system on bounded domains
  In: Proceedings of the Royal Society of Edinburgh Section A-Mathematics (2023)
  ISSN: 0308-2105
  DOI: 10.1017/prm.2023.85
• Conti M., Liverani L., Pata V.:
  On the Moore-Gibson-Thompson Equation with Memory with Nonconvex Kernels
  In: Indiana University Mathematics Journal 72 (2023), p. 1-27
  ISSN: 0022-2518
  DOI: 10.1512/iumj.2023.72.9330
• Dell’Oro F., Liverani L., Pata V.:
  On the Regularized Moore-Gibson-Thompson Equation
  In: Discrete and Continuous Dynamical Systems. Series S 16 (2023), p. 2326-2338
  ISSN: 1937-1632
  DOI: 10.3934/dcdss.2023025
• Liverani L., Quintanilla R.:
  Thermoelasticity with temperature and microtemperatures with fading memory
  In: Mathematics and Mechanics of Solids 28 (2023), p. 1255-1273
  ISSN: 1081-2865
  DOI: 10.1177/10812865221115359

2022

• Conti M., Liverani L., Pata V.:
  Erratum: THERMOELASTICITY WITH ANTIDISSIPATION (Discrete and Continuous Dynamical Systems - Series S (2022) 15:8 (2173-2188))
  In: Discrete and Continuous Dynamical Systems. Series S 15 (2022), p. 2429-2431
  ISSN: 1937-1632
  DOI: 10.3934/dcdss.2022125
• Conti M., Liverani L., Pata V.:
  On the Optimal Decay Rate of the Weakly Damped Wave Equation
  In: Communications on Pure and Applied Analysis 21 (2022), p. 3421-3424
  ISSN: 1534-0392
  DOI: 10.3934/cpaa.2022107
• Conti M., Dell’Oro F., Liverani L., Pata V.:
  Spectral Analysis and Stability of the Moore-Gibson-Thompson-Fourier Model
  In: Journal of Dynamics and Differential Equations (2022)
  ISSN: 1040-7294
  DOI: 10.1007/s10884-022-10164-z
• Conti M., Liverani L., Pata V.:
  Thermoelasticity with Antidissipation
  In: Discrete and Continuous Dynamical Systems. Series S 15 (2022), p. 2173-2188
  ISSN: 1937-1632
  DOI: 10.3934/dcdss.2022040

2021

• Conti M., Liverani L., Pata V.:
  A note on the energy transfer in coupled differential systems
  In: Communications on Pure and Applied Analysis 20 (2021), p. 1821-1831
  ISSN: 1534-0392
  DOI: 10.3934/cpaa.2021042
• Conti M., Liverani L., Pata V.:
  The MGT-Fourier model in the supercritical case
  In: Journal of Differential Equations 301 (2021), p. 543-567
  ISSN: 0022-0396
  DOI: 10.1016/j.jde.2021.08.030