23 citations · 78 across the 16 of their papers we have counts for
17 papers
Local Asymptotic Patterns for Viscous Approximations of Conservation Laws
Alberto Bressan, Laura Caravenna, Wen Shen
Solutions to hyperbolic conservation laws can be approximated in many different ways: by vanishing viscosity, relaxations, discrete or semi-discrete numerical schemes, approximatio…
On the regularity of continuous solutions to multidimensional scalar conservation laws with bounded source
Fabio Ancona, Laura Caravenna, Alexander J. Cliffe +1
We prove the Hölder regularity of continuous isentropic solutions to multi-dimensional scalar balance laws when the source term is bounded and the flux satisfies general assumption…
Consensus in Multiagent Systems under communication failure
Mohamed Bentaibi, Laura Caravenna, Jean-Paul A. Gauthier +1
We consider multi-agent systems with cooperative interactions and study the convergence to consensus in the case of time-dependent connections, with possible communication failure.…
SBV regularity of Entropy Solutions for Hyperbolic Systems of Balance Laws with General Flux function
Fabio Ancona, Laura Caravenna, Andrea Marson
We prove that vanishing viscosity solutions to smooth non-degenerate systems of balance laws having small bounded variation, in one space dimension, must be functions of special bo…
Eulerian, Lagrangian and broad continuous solutions to a balance law with non convex flux II
Giovanni Alberti, Stefano Bianchini, Laura Caravenna
We consider a *continuous* solution of the balance law \[ \partial_{\mathit t} u + \partial_{\mathit x} (f(u)) = g\] in one space dimension, where the flux function is of c…
Hölder regularity of continuous solutions to balance laws and applications in the Heisenberg group
Laura Caravenna, Elio Marconi, Andrea Pinamonti
We prove Hölder regularity of any continuous solution to a -D scalar balance law , when the source term is bounded and the flux is nonlinear of o…
Exponential Stability of Large BV Solutions in a Model of Granular flow
Fabio Ancona, Laura Caravenna, Cleopatra Christoforou
We consider a system of hyperbolic balance laws, in one-space dimension, that describes the evolution of a granular material with slow erosion and deposition. The dynam…
On the Lebesgue measure of the boundary of the evoluted set
Francesco Boarotto, Laura Caravenna, Francesco Rossi +1
The evoluted set is the set of configurations reached from an initial set via a fixed flow for all times in a fixed interval. We find conditions on the initial set and on the flow…
A Directional Lipschitz Extension Lemma, with Applications to Uniqueness and Lagrangianity for the Continuity Equation
Laura Caravenna, Gianluca Crippa
We prove a Lipschitz extension lemma in which the extension procedure simultaneously preserves the Lipschitz continuity for two non-equivalent distances. The two distances under co…
On the structure of solutions for general hyperbolic systems of balance laws
Fabio Ancona, Laura Caravenna, Andrea Marson
The paper describes the qualitative structure of BV entropy solutions of a strictly hyperbolic system of balance laws with characteristic fields either piecewise genuinely nonlinea…
Uniqueness and Lagrangianity for solutions with lack of integrability of the continuity equation
Laura Caravenna, Gianluca Crippa
We deal with the uniqueness of distributional solutions to the continuity equation with a Sobolev vector field and with the property of being a Lagrangian solution, that means tran…
Eulerian, Lagrangian and Broad continuous solutions to a balance law with non convex flux I
G. Alberti, S. Bianchini, L. Caravenna
We discuss different notions of continuous solutions to the balance law \[u_t + (f(u ))_x =g \] with bounded, , extending previous works relative to the flux $f(u)=…
Schaeffer's regularity theorem for scalar conservation laws does not extend to systems
Laura Caravenna, Laura 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 initi…
A note on regularity and failure of regularity for systems of conservation laws via Lagrangian formulation
Laura Caravenna
The paper recalls two of the regularity results for Burgers' equation, and discusses what happens in the case of genuinely nonlinear, strictly hyperbolic systems of conservation la…
New interaction estimates for the Baiti-Jenssen system
Laura Caravenna, Laura 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 comp…
Intrinsic Lipschitz graphs in Heisenberg groups and continuous solutions of a balance equation
Francesco Bigolin, Laura Caravenna, Francesco Serra Cassano
In this paper we provide a characterization of intrinsic Lipschitz graphs in the sub-Riemannian Heisenberg groups in terms of their distributional gradients. Moreover, we prove the…
SBV Regularity for Genuinely Nonlinear, Strictly Hyperbolic Systems of Conservation Laws in one space dimension
Stefano Bianchini, Laura Caravenna
We prove that if is the entropy solution to a strictly hyperbolic system of conservation laws with genuinely nonlinear characteri…