My Publications

Journal Articles

  1. Z. Li, K. Liu, L. Liverani, and E. Zuazua
    "Universal Approximation of Dynamical Systems by Semiautonomous Neural ODEs and Applications"
    SIAM Journal on Numerical Analysis, vol. 64, pp. 193--223
    2025 📄 DOI
  2. A. Di Primio, and L. Liverani
    "Large-time asymptotics of the regularized Moore-Gibson-Thompson equation with Gurtin-Pipkin thermal law"
    Discrete and Continuous Dynamical Systems - Series S
    2026 To appear 📄 DOI
  3. T. Crin-Barat, L. Liverani, L.-Y. Shou, and E. Zuazua
    "Large-time asymptotics for hyperbolic systems with non-symmetric relaxation: An algorithmic approach"
    Journal de Mathématiques Pures et Appliquées, vol. 202, 103757
    2025 📄 DOI
  4. L. Liverani, Y. Mammeri, V. Pata and R. Quintanilla
    "On the linearized Whitham–Broer–Kaup system on bounded domains"
    Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol. 155, pp. 104–123
    2025 📄 DOI
  5. V. Felli, L. Liverani, and R. Ognibene
    "Quantitative spectral stability for the Neumann Laplacian in domains with small holes"
    J. Funct. Anal., vol. 288, no. 6, Paper No. 110817
    2025 📄 DOI
  6. F. Dell'Oro, L. Liverani, V. Pata, and R. Quintanilla
    "On the double Moore–Gibson–Thompson system of thermoviscoelasticity"
    Studies in Applied Mathematics, vol. 154, no. 1, e12784
    2025 📄 DOI
  7. F. Dell'Oro, L. Liverani, V. Pata, and R. Quintanilla
    "Global attractors for Moore-Gibson-Thompson thermoelastic extensible beams and Berger plates"
    Nonlinear Analysis Real World Applications, vol. 84, Paper No. 104298
    2025 📄 DOI
  8. N. Bazarra, J. R. Fernández, L. Liverani, and R. Quintanilla
    "Analysis of a thermoelastic problem with the Moore-Gibson-Thompson microtemperatures"
    J. Comput. Appl. Math., vol. 438, Paper No. 115571
    2024 📄 DOI
  9. P. F. Antonietti, L. Liverani and V. Pata
    "Lack of superstable trajectories in linear viscoelasticity: A numerical approach"
    Numer. Math., vol. 153, no. 4, pp. 611–633
    2023 📄 DOI
  10. F. Dell'Oro, L. Liverani and V. Pata
    "On the regularized Moore-Gibson-Thompson equation"
    Discrete Contin. Dyn. Syst. Ser. S
    2023 📄 DOI
  11. M. Conti, L. Liverani and V. Pata
    "On the Moore-Gibson-Thompson equation with memory with nonconvex kernels"
    Indiana Univ. Math. J., vol. 72, pp. 1–27
    2023 📄 DOI
  12. M. Conti, L. Liverani, F. Dell'Oro, and V. Pata
    "Spectral analysis and stability of the Moore-Gibson-Thompson-Fourier model"
    J. Dynam. Differential Equations
    2022 📄 DOI
  13. M. Conti, L. Liverani and V. Pata
    "On the optimal decay rate of the weakly damped wave equation"
    Commun. Pure Appl. Anal., vol. 21, pp. 3421–3424
    2022 📄 DOI
  14. L. Liverani and R. Quintanilla
    "Thermoelasticity with temperature and microtemperatures with fading memory"
    Math. Mech. Solids, vol. 28, pp. 1255–1273
    2022 📄 DOI
  15. M. Conti, L. Liverani and V. Pata
    "Correction to 'Thermoelasticity with antidissipation'"
    Discrete Contin. Dyn. Syst. Ser. S, vol. 15, pp. 2429–2431
    2022 📄 DOI
  16. M. Conti, L. Liverani and V. Pata
    "Thermoelasticity with antidissipation"
    Discrete Contin. Dyn. Syst. Ser. S, vol. 15, pp. 2173–2188
    2022 📄 DOI
  17. M. Conti, L. Liverani and V. Pata
    "The MGT-Fourier model in the supercritical case"
    J. Differential Equations, vol. 301, pp. 543–567
    2021 📄 DOI
  18. M. Conti, L. Liverani and V. Pata
    "A note on the energy transfer in coupled differential systems"
    Commun. Pure Appl. Anal., vol. 20, pp. 1821–1831
    2021 📄 DOI

Preprints

  1. V. Felli, L. Liverani, and R. Ognibene
    "On the splitting of Neumann eigenvalues in perforated domains"
    ArXiv
    2026 📄 DOI
  2. L. Liverani, M. Steynberg, and E. Zuazua
    "HYCO: Hybrid-Cooperative Learning for Data-Driven PDE Modeling"
    ArXiv
    2026 📄 DOI
  3. F. Dell'Oro, L. Liverani, and V. Pata
    "Abstract damped wave equations: The optimal decay rate"
    ArXiv
    2024 📄 DOI