Dr. Lorenzo Liverani
Email • PhD in Mathematics, Politecnico di Milano
Wellposedness and asymptotic behavior of hyperbolic PDEs, semigroup theory, spectral stability problems for elliptic operators
Postdoctoral Researcher
Funded by Alexander von Humboldt Stiftung/Foundation
Room 03.361 | FAU DCN-AvH, Chair for Dynamics, Control, Machine Learning and Numerics – Alexander von Humboldt Professorship
FAU MoD member, Research Center for Mathematics of Data
Friedrich-Alexander-Universität Erlangen-Nürnberg
Naturwissenschaftliche Fakultät. Department Mathematik
Research Gate | ORCID | Personal site | LinkedIn
In 2023 I have obtained my PhD at Politecnico di Milano, under the supervision of professor Vittorino Pata.
After a one-year postdoc at the Università degli Studi Milano Bicocca, under the supervision of professor Veronica Felli, I have joined the Chair for Dynamics, Control, Machine Learning and Numerics at FAU as an Alexander von Humboldt postdoctoral researcher.
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Research interests
My research interests focus on
• the wellposedness and asymptotic behavior of hyperbolic partial differential equations
• the wellposedness and asymptotic behavior on semigroup theory
• spectral stability problems for elliptic operators
Projects
• Chair for Dynamics, Control, Machine Learning and Numerics – AvH (2024 – now)
News / Initiatives
#MLPDES25: Machine Learning and PDEs Workshop (2026)
Authors: Lorenzo Liverani (Organizing Committee)
Date: June 22 – 24, 2026
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HYCO: Hybrid-Cooperative Learning for PDEs. FAU MoD Workshop, Erlangen – Bavaria (Germany)
Authors: Lorenzo Liverani
Date: September 23, 2025
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Stability of Hyperbolic Systems with Non-Symmetric Relaxation. FAU MoD Lecture & Workshop: AI for maths and maths for AI
Authors: François Charton, Lorenzo Liverani
Date: June 24, 2025
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#MLPDES25: Machine Learning and PDEs Workshop (2025)
Authors: Lorenzo Liverani (Organizing Committee, Speaker)
Date: April 28 – 30, 2025
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Energy Estimates, Semigroups, and The Weakly Damped Wave Equation. FAU DCN-AvH Seminar
Authors: Lorenzo Liverani
Date: February 29, 2024
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Publications
2026
- , , , :
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
BibTeX: Download - , , :
HYCO: Hybrid-Cooperative Learning for Data-Driven PDE Modeling
(2026)
BibTeX: Download - , , :
HYCO: Hybrid-Cooperative Learning for Data-Driven PDE Modeling
(2026)
Open Access: https://arxiv.org/abs/2509.14123v1
BibTeX: Download - , :
HYCO: A formalism for Hybrid-Cooperative PDE modelling
(2026)
BibTeX: Download
2025
- , , , :
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
BibTeX: Download - , , , :
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
BibTeX: Download - , , :
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
BibTeX: Download
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
BibTeX: Download - , , , :
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
BibTeX: Download
2023
- , , :
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
BibTeX: Download - 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
BibTeX: Download - 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
BibTeX: Download - 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
BibTeX: Download - 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
BibTeX: Download
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
BibTeX: Download - 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
BibTeX: Download - 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
BibTeX: Download - 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
BibTeX: Download
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
BibTeX: Download - 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
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