36 citations · 140 across the 28 of their papers we have counts for
5 papers · 1 filter
Generalized Characteristics for Finite Entropy Solutions of Burgers' Equation
Andres A. Contreras Hip, Xavier Lamy, Elio Marconi
We prove the existence of generalized characteristics for weak, not necessarily entropic, solutions of Burgers' equation \[ \partial_t u +\partial_x \frac{u^2}{2} =0, \] whose entr…
New regularity results for scalar conservation laws, and applications to a source-destination model for traffic flows on networks
Simone Dovetta, Elio Marconi, Laura 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 flu…
Initial-boundary value problems for merely bounded nearly incompressible vector fields in one space dimension
Simone Dovetta, Elio Marconi, Laura 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 t…
Characterization of minimizers of Aviles-Giga functionals in special domains
Elio Marconi
We consider the singularly perturbed problem on bounded domains . Un…
Differentiability properties of the flow of 2d autonomous vector fields
Elio Marconi
We investigate under which assumptions the flow associated to autonomous planar vector fields inherits the Sobolev or BV regularity of the vector field. We consider nearly incompre…