Lorenzo Liverani
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Publications
Journal Articles
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. 193โ223
2026
๐ PAPER
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, vol. 26, pp. 216โ242
2026
๐ PAPER
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 Mathรฉmatiques Pures et Appliquรฉes, vol. 202, 103757
2025
๐ PAPER
L. Liverani
, Y. Mammeri, V. Pata and R. Quintanilla
"On the linearized WhithamโBroerโKaup system on bounded domains"
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol. 155, pp. 104โ123
2025
๐ PAPER
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
๐ PAPER
F. Dell'Oro,
L. Liverani
, V. Pata, and R. Quintanilla
"On the double MooreโGibsonโThompson system of thermoviscoelasticity"
Studies in Applied Mathematics, vol. 154, no. 1, e12784
2025
๐ PAPER
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
๐ PAPER
N. Bazarra, J. R. Fernรกndez,
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
๐ PAPER
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. 611โ633
2023
๐ PAPER
F. Dell'Oro,
L. Liverani
and V. Pata
"On the regularized Moore-Gibson-Thompson equation"
Discrete Contin. Dyn. Syst. Ser. S, vol. 16, no. 9, pp. 2326โ2338
2023
๐ PAPER
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. 1โ27
2023
๐ PAPER
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, vol. 36, pp. 775โ795
2022
๐ PAPER
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. 3421โ3424
2022
๐ PAPER
L. Liverani
and R. Quintanilla
"Thermoelasticity with temperature and microtemperatures with fading memory"
Math. Mech. Solids, vol. 28, pp. 1255โ1273
2022
๐ PAPER
M. Conti,
L. Liverani
and V. Pata
"Correction to 'Thermoelasticity with antidissipation'"
Discrete Contin. Dyn. Syst. Ser. S, vol. 15, pp. 2429โ2431
2022
๐ PAPER
M. Conti,
L. Liverani
and V. Pata
"Thermoelasticity with antidissipation"
Discrete Contin. Dyn. Syst. Ser. S, vol. 15, pp. 2173โ2188
2022
๐ PAPER
M. Conti,
L. Liverani
and V. Pata
"The MGT-Fourier model in the supercritical case"
J. Differential Equations, vol. 301, pp. 543โ567
2021
๐ PAPER
M. Conti,
L. Liverani
and V. Pata
"A note on the energy transfer in coupled differential systems"
Commun. Pure Appl. Anal., vol. 20, pp. 1821โ1831
2021
๐ PAPER
Preprints
A. รlvarez-Lรณpez,
L. Liverani
, and E. Zuazua
"Constructive interpolation and generalization rates for neural ODEs: a control perspective"
ArXiv
2026
๐ PAPER
X. Gong, A. Keimer,
L. Liverani
, and H. Matin
"Existence and uniqueness of nonlocal nonlinear conservation laws via fixed-point methods"
ArXiv
2026
๐ PAPER
V. Felli,
L. Liverani
, and R. Ognibene
"On the splitting of Neumann eigenvalues in perforated domains"
ArXiv
2026
๐ PAPER
L. Liverani
, and E. Zuazua
"HYCO: Hybrid-Cooperative Learning for Data-Driven PDE Modeling"
ArXiv
2026
๐ PAPER
D. Lopez-Montero,
L. Liverani
, E. Zuazua, and X. Kobeleva
"Balancing data fidelity and interpretability of whole-brain dynamics via hybrid generative modeling"
Submitted for review
2026
Under Review
F. Dell'Oro,
L. Liverani
, and V. Pata
"Abstract damped wave equations: The optimal decay rate"
ArXiv
2024
๐ PAPER