Laura Spinolo
Senior Researcher
Since 2020 I am Senior Researcher at CNR-IMATI. For further details concerning my cv and research activity please see my personal webpage
Research Activity
My reserach activity focuses on partial differential equations, mainly of hyperbolic type. In particular, I have been recently working on the following topis:
-nonlinear systems of conservation laws;
- transport equations with low regularity coefficients;Â
- fluido-dynamic traffic models.Â
Projects
Publications
2023, Journal article
Nonlocal traffic models with general kernels: Singular limit, entropy admissibility, and convergence rate
M. Colombo, G. Crippa, E. Marconi, and L.V. Spinolo
Nonlocal conservation laws (the signature feature being that the flux function depends on the solution through the convolution with a given kernel) are extensively used in the modeling of vehicular tr...
CNR@People | DOI: 10.1007/s00205-023-01845-0
2022, Journal article
Initial-boundary value problems for merely bounded nearly incompressible vector fields in one space dimension
S. Dovetta, E. Marconi, and L.V. Spinolo
We establish existence and uniqueness results for initial-boundary value problems for transport equations in one space dimension with nearly incompressible velocity fields, under the sole assumption t...
CNR@People | DOI: 10.1016/j.jde.2021.10.037
2022, Journal article
New regularity results for scalar conservation laws, and applications to a source-destination model for traffic flows on networks
S. Dovetta, E. Marconi, and L.V. Spinolo
We focus on entropy admissible solutions of scalar conservation laws in one space dimension and establish new regularity results with respect to time. First, we assume that the flux function f is stri...
CNR@People | DOI: 10.1137/21M1434283
2021, Journal article
Local limit of nonlocal traffic models: Convergence results and total variation blow-up
M. Colombo, G. Crippa, E. Marconi, and V. Spinolo
Consider a nonlocal conservation law where the flux function depends on the convolution of the solution with a given kernel. In the singular local limit obtained by letting the convolution kernel conv...
CNR@People | DOI: 10.1016/j.anihpc.2020.12.002
2021, Journal article
On the role of numerical viscosity in the study of the local limit of nonlocal conservation laws
M. Colombo, G. Crippa, M. Graff, and L.V. Spinolo
We deal with the numerical investigation of the local limit of nonlocal conservation laws. Previous numerical experiments seem to suggest that the solutions of the nonlocal problems converge to the en...
CNR@People | DOI: 10.1051/m2an/2021073
2020, Journal article
Characteristic boundary layers for mixed hyperbolic-parabolic systems in one space dimension and applications to the Navier-Stokes and MHD equations
S. Bianchini and L.V. Spinolo
We provide a detailed analysis of the boundary layers for mixed hyperbolic-parabolic systems in one space dimension and small amplitude regimes. As an application of our results, we describe the solut...
CNR@People | DOI: 10.1002/cpa.21892
2019, Journal article
On the singular local limit for conservation laws with nonlocal fluxes
M. Colombo, G. Crippa, and L.V. Spinolo
We give an answer to a question posed in Amorim et al. (ESAIM Math Model Numer Anal 49(1):19-37, 2015), which can loosely speaking, be formulated as follows: consider a family of continuity equations ...
CNR@People | DOI: 10.1007/s00205-019-01375-8
2018, Journal article
Optimal strategies for a time-dependent harvesting problem
G. M Coclite, M. Garavello, and L. V. Spinolo
We focus on an optimal control problem, introduced by Bressan and Shen in [5] as a model for fish harvesting. We consider the time-dependentcase and we establish existence and uniqueness of an optimal...
CNR@People | DOI: 10.3934/dcdss.2018053
2018, Journal article
Quantitative estimates on localized finite differences for the fractional Poisson problem, and applications to regularity and spectral stability
G. Akagi, G. Schimperna, A. Segatti, and L.V. Spinolo
We establish new quantitative estimates for localized finite differences of solutions to thePoisson problem for the fractional Laplace operator with homogeneous Dirichlet conditions of solidtype settl...
CNR@People | DOI: 10.4310/CMS.2018.v16.n4.a2
2017, Journal article
A mathematical model for piracy control through police response
G.M. Coclite, M. Garavello, and L.V.Spinolo
We introduce a model describing the dynamics and interactions of three populations of ships (pirates ships, commercial cargos, and police watercrafts) in a marine region. We establish well-posedness o...
CNR@People | DOI: 10.1007/s00030-017-0471-9
2017, Journal article
Initial-boundary value problems for nearly incompressible vector fields, and applications to the Keyfitz and Kranzer system
A.P. Choudhury, G. Crippa, and L.V. Spinolo
We establish existence and uniqueness results for initial-boundary value problems with nearly incompressiblevector fields. We then apply our results to establish well-posedness of the initial-boundary...
CNR@People | DOI: 10.1007/s00033-017-0883-8
2017, Journal article
Optimality of integrability estimates for advection-diffusion equations
S. Bianchini, M. Colombo, G. Crippa, and L.V. Spinolo
We discuss L-p integrability estimates for the solution u of the advection-diffusion equation partial derivative(t)u+div(bu) =Delta u, where the velocity field b is an element of (LtLxq)-L-r. We first...
CNR@People | DOI: 10.1007/s00030-017-0455-9
2017, Journal article
Schaeffer's regularity theorem for scalar conservation laws does not extend to systems
L. Caravenna and L.V. Spinolo
Schaeffer's regularity theorem for scalar conservation laws can be loosely speaking formulated as follows. Assume that the flux is uniformly convex, then for a generic smooth initial datum the admissi...
CNR@People | DOI: 10.1512/iumj.2017.66.6010
2016, Journal article
New interaction estimates for the Baiti-Jenssen system
L. Caravenna and L. V. Spinolo
We establish new interaction estimates for a system introduced by Baiti and Jenssen. These estimates are pivotal to the analysis of the wave front-tracking approximation. In a companion paper we use t...
CNR@People | DOI: 10.3934/nhm.2016.11.263
2015, Journal article
Accurate numerical schemes for approximating initial-boundary value problems for systems of conservation laws
S. Mishra and L. V. Spinolo
Solutions of initial-boundary value problems for systems of conservation laws depend on the underlying viscous mechanism, namely different viscosity operators lead to different limit solutions. Standa...
CNR@People | DOI: 10.1142/S0219891615500034
2014, Journal article
Initial-boundary value problems for continuity equations with BV coefficients
G. Crippa, C. Donadello, and L. V. Spinolo
We establish well-posedness of initial-boundary value problems for continuity equations with BV (bounded total variation) coefficients. We do not prescribe any condition on the orientation of the coef...
CNR@People | DOI: 10.1016/j.matpur.2013.11.002
2014, Journal article
On the extension property of Reifenberg-flat domains
A. Lemenant, E. Milakis, and L. V. Spinolo
We provide a detailed proof of the fact that any open set whose boundary is sufficiently flat in the sense of Reifenberg is also Jones-flat, and hence it admits an extension operator. We discuss vario...
CNR@People | DOI: 10.5186/aasfm.2014.3907
2013, Journal article
Boundary layers for self-similar viscous approximations of nonlinear hyperbolic systems
C. Christoforou and L. V. Spinolo
We provide a precise description of the set of residual boundary conditions generated by the self-similar viscous approximation introduced by Dafermos et al. We then apply our results, valid for both ...
CNR@People | DOI: 10.1090/S0033-569X-2013-01284-6
2013, Journal article
Spectral stability estimates for the Dirichlet and Neumann Laplacian in rough domains
A. Lemenant, E. Milakis, and L. V. Spinolo
In this paper we establish new quantitative stability estimates with respect to domain perturbations for all the eigenvalues of both the Neumann and the Dirichlet Laplacian. Our main results follow fr...
CNR@People | DOI: 10.1016/j.jfa.2013.02.006
2011, Journal article
A uniqueness criterion for viscous limits of boundary Riemann problems
C. Christoforou and L. V. Spinolo
We deal with the initial boundary value problem for systems of conservation laws in one space dimension and we focus on the boundary Riemann problem. It is known that, in general, different viscous ap...
CNR@People | DOI: 10.1142/S0219891611002482
2011, Journal article
Invariant manifolds for a singular ordinary differential equation
S. Bianchini and L. V. Spinolo
We study the singular ordinary differential equationdU/dt = F(U)/z(U) + G(U).The equation is singular because z(U) can attain the value 0. We focus onthe solutions of the above equation thatbelong to ...
CNR@People | DOI: 10.1016/j.jde.2010.11.010
Nonlocal traffic models with general kernels: Singular limit, entropy admissibility, and convergence rate
M. Colombo, G. Crippa, E. Marconi, and L.V. Spinolo
Nonlocal conservation laws (the signature feature being that the flux function depends on the solution through the convolution with a given kernel) are extensively used in the modeling of vehicular tr...
CNR@People | DOI: 10.1007/s00205-023-01845-0
2022, Journal article
Initial-boundary value problems for merely bounded nearly incompressible vector fields in one space dimension
S. Dovetta, E. Marconi, and L.V. Spinolo
We establish existence and uniqueness results for initial-boundary value problems for transport equations in one space dimension with nearly incompressible velocity fields, under the sole assumption t...
CNR@People | DOI: 10.1016/j.jde.2021.10.037
2022, Journal article
New regularity results for scalar conservation laws, and applications to a source-destination model for traffic flows on networks
S. Dovetta, E. Marconi, and L.V. Spinolo
We focus on entropy admissible solutions of scalar conservation laws in one space dimension and establish new regularity results with respect to time. First, we assume that the flux function f is stri...
CNR@People | DOI: 10.1137/21M1434283
2021, Journal article
Local limit of nonlocal traffic models: Convergence results and total variation blow-up
M. Colombo, G. Crippa, E. Marconi, and V. Spinolo
Consider a nonlocal conservation law where the flux function depends on the convolution of the solution with a given kernel. In the singular local limit obtained by letting the convolution kernel conv...
CNR@People | DOI: 10.1016/j.anihpc.2020.12.002
2021, Journal article
On the role of numerical viscosity in the study of the local limit of nonlocal conservation laws
M. Colombo, G. Crippa, M. Graff, and L.V. Spinolo
We deal with the numerical investigation of the local limit of nonlocal conservation laws. Previous numerical experiments seem to suggest that the solutions of the nonlocal problems converge to the en...
CNR@People | DOI: 10.1051/m2an/2021073
2020, Journal article
Characteristic boundary layers for mixed hyperbolic-parabolic systems in one space dimension and applications to the Navier-Stokes and MHD equations
S. Bianchini and L.V. Spinolo
We provide a detailed analysis of the boundary layers for mixed hyperbolic-parabolic systems in one space dimension and small amplitude regimes. As an application of our results, we describe the solut...
CNR@People | DOI: 10.1002/cpa.21892
2019, Journal article
On the singular local limit for conservation laws with nonlocal fluxes
M. Colombo, G. Crippa, and L.V. Spinolo
We give an answer to a question posed in Amorim et al. (ESAIM Math Model Numer Anal 49(1):19-37, 2015), which can loosely speaking, be formulated as follows: consider a family of continuity equations ...
CNR@People | DOI: 10.1007/s00205-019-01375-8
2018, Journal article
Optimal strategies for a time-dependent harvesting problem
G. M Coclite, M. Garavello, and L. V. Spinolo
We focus on an optimal control problem, introduced by Bressan and Shen in [5] as a model for fish harvesting. We consider the time-dependentcase and we establish existence and uniqueness of an optimal...
CNR@People | DOI: 10.3934/dcdss.2018053
2018, Journal article
Quantitative estimates on localized finite differences for the fractional Poisson problem, and applications to regularity and spectral stability
G. Akagi, G. Schimperna, A. Segatti, and L.V. Spinolo
We establish new quantitative estimates for localized finite differences of solutions to thePoisson problem for the fractional Laplace operator with homogeneous Dirichlet conditions of solidtype settl...
CNR@People | DOI: 10.4310/CMS.2018.v16.n4.a2
2017, Journal article
A mathematical model for piracy control through police response
G.M. Coclite, M. Garavello, and L.V.Spinolo
We introduce a model describing the dynamics and interactions of three populations of ships (pirates ships, commercial cargos, and police watercrafts) in a marine region. We establish well-posedness o...
CNR@People | DOI: 10.1007/s00030-017-0471-9
2017, Journal article
Initial-boundary value problems for nearly incompressible vector fields, and applications to the Keyfitz and Kranzer system
A.P. Choudhury, G. Crippa, and L.V. Spinolo
We establish existence and uniqueness results for initial-boundary value problems with nearly incompressiblevector fields. We then apply our results to establish well-posedness of the initial-boundary...
CNR@People | DOI: 10.1007/s00033-017-0883-8
2017, Journal article
Optimality of integrability estimates for advection-diffusion equations
S. Bianchini, M. Colombo, G. Crippa, and L.V. Spinolo
We discuss L-p integrability estimates for the solution u of the advection-diffusion equation partial derivative(t)u+div(bu) =Delta u, where the velocity field b is an element of (LtLxq)-L-r. We first...
CNR@People | DOI: 10.1007/s00030-017-0455-9
2017, Journal article
Schaeffer's regularity theorem for scalar conservation laws does not extend to systems
L. Caravenna and L.V. Spinolo
Schaeffer's regularity theorem for scalar conservation laws can be loosely speaking formulated as follows. Assume that the flux is uniformly convex, then for a generic smooth initial datum the admissi...
CNR@People | DOI: 10.1512/iumj.2017.66.6010
2016, Journal article
New interaction estimates for the Baiti-Jenssen system
L. Caravenna and L. V. Spinolo
We establish new interaction estimates for a system introduced by Baiti and Jenssen. These estimates are pivotal to the analysis of the wave front-tracking approximation. In a companion paper we use t...
CNR@People | DOI: 10.3934/nhm.2016.11.263
2015, Journal article
Accurate numerical schemes for approximating initial-boundary value problems for systems of conservation laws
S. Mishra and L. V. Spinolo
Solutions of initial-boundary value problems for systems of conservation laws depend on the underlying viscous mechanism, namely different viscosity operators lead to different limit solutions. Standa...
CNR@People | DOI: 10.1142/S0219891615500034
2014, Journal article
Initial-boundary value problems for continuity equations with BV coefficients
G. Crippa, C. Donadello, and L. V. Spinolo
We establish well-posedness of initial-boundary value problems for continuity equations with BV (bounded total variation) coefficients. We do not prescribe any condition on the orientation of the coef...
CNR@People | DOI: 10.1016/j.matpur.2013.11.002
2014, Journal article
On the extension property of Reifenberg-flat domains
A. Lemenant, E. Milakis, and L. V. Spinolo
We provide a detailed proof of the fact that any open set whose boundary is sufficiently flat in the sense of Reifenberg is also Jones-flat, and hence it admits an extension operator. We discuss vario...
CNR@People | DOI: 10.5186/aasfm.2014.3907
2013, Journal article
Boundary layers for self-similar viscous approximations of nonlinear hyperbolic systems
C. Christoforou and L. V. Spinolo
We provide a precise description of the set of residual boundary conditions generated by the self-similar viscous approximation introduced by Dafermos et al. We then apply our results, valid for both ...
CNR@People | DOI: 10.1090/S0033-569X-2013-01284-6
2013, Journal article
Spectral stability estimates for the Dirichlet and Neumann Laplacian in rough domains
A. Lemenant, E. Milakis, and L. V. Spinolo
In this paper we establish new quantitative stability estimates with respect to domain perturbations for all the eigenvalues of both the Neumann and the Dirichlet Laplacian. Our main results follow fr...
CNR@People | DOI: 10.1016/j.jfa.2013.02.006
2011, Journal article
A uniqueness criterion for viscous limits of boundary Riemann problems
C. Christoforou and L. V. Spinolo
We deal with the initial boundary value problem for systems of conservation laws in one space dimension and we focus on the boundary Riemann problem. It is known that, in general, different viscous ap...
CNR@People | DOI: 10.1142/S0219891611002482
2011, Journal article
Invariant manifolds for a singular ordinary differential equation
S. Bianchini and L. V. Spinolo
We study the singular ordinary differential equationdU/dt = F(U)/z(U) + G(U).The equation is singular because z(U) can attain the value 0. We focus onthe solutions of the above equation thatbelong to ...
CNR@People | DOI: 10.1016/j.jde.2010.11.010
2016, Conference proceedings
An overview on the approximation of boundary Riemann problems through physical viscosity
S. Bianchini and L. V. Spinolo
This note aims at providing an overview of some recent results concerning the viscous approximation of so-called boundary Riemann problems for nonlinear systems of conservation laws in small total var...
CNR@People | DOI: 10.1007/s00574-016-0127-0
2015, Conference proceedings
A counter-example concerning regularity properties for systems of conservation laws
L. Caravenna and L.V. Spinolo
We exhibit an explicit counter-example which rules the possibility of extending to systems of conservation laws a regularity property of scalar conservation laws known as Schaeffer's Theorem. Loosely ...
CNR@People | DOI: 10.1002/pamm.201510302
2014, Conference proceedings
A note on the initial-boundary value problem for continuity equations with rough coefficients
G. Crippa, C. Donadello, and L. V. Spinolo
In this note we establish the existence of solutions of initial-boundaryvalue problems for continuity equations with low regularity coefficients. Wealso announce a uniqueness result and some related c...
CNR@People | Link
2012, Conference proceedings
On the physical and the self-similar viscous approximation of a boundary Riemann problem
C. Christoforou and L. V. Spinolo
We deal with the viscous approximation of a system of conservation laws in one space dimension and we focus on initial-boundary value problems. It is known that, in general, different viscous approxim...
CNR@People | Link
2011, Conference proceedings
Existence and uniqueness results for the continuity equation and applications to the chromatography system
L. Ambrosio, G. Crippa, A. Figalli, and L. V. Spinolo
We discuss some new well-posedness results for the continuity equation in arbitrary space dimension and we then illustrate applications to a system of conservation laws in one space dimension known as...
CNR@People | DOI: 10.1007/978-1-4419-9554-4_8
An overview on the approximation of boundary Riemann problems through physical viscosity
S. Bianchini and L. V. Spinolo
This note aims at providing an overview of some recent results concerning the viscous approximation of so-called boundary Riemann problems for nonlinear systems of conservation laws in small total var...
CNR@People | DOI: 10.1007/s00574-016-0127-0
2015, Conference proceedings
A counter-example concerning regularity properties for systems of conservation laws
L. Caravenna and L.V. Spinolo
We exhibit an explicit counter-example which rules the possibility of extending to systems of conservation laws a regularity property of scalar conservation laws known as Schaeffer's Theorem. Loosely ...
CNR@People | DOI: 10.1002/pamm.201510302
2014, Conference proceedings
A note on the initial-boundary value problem for continuity equations with rough coefficients
G. Crippa, C. Donadello, and L. V. Spinolo
In this note we establish the existence of solutions of initial-boundaryvalue problems for continuity equations with low regularity coefficients. Wealso announce a uniqueness result and some related c...
CNR@People | Link
2012, Conference proceedings
On the physical and the self-similar viscous approximation of a boundary Riemann problem
C. Christoforou and L. V. Spinolo
We deal with the viscous approximation of a system of conservation laws in one space dimension and we focus on initial-boundary value problems. It is known that, in general, different viscous approxim...
CNR@People | Link
2011, Conference proceedings
Existence and uniqueness results for the continuity equation and applications to the chromatography system
L. Ambrosio, G. Crippa, A. Figalli, and L. V. Spinolo
We discuss some new well-posedness results for the continuity equation in arbitrary space dimension and we then illustrate applications to a system of conservation laws in one space dimension known as...
CNR@People | DOI: 10.1007/978-1-4419-9554-4_8
