6 papers · 1 filter
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…
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…
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 assumptio…
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…
SBV-like regularity of Entropy Solutions for a Scalar Balance Law
Fabio Ancona, Laura Caravenna, Andrea Marson
In this note we discuss the SBV-regularity for a scalar balance law in one space dimension as a case study in order to explain the strategy that we apply in a separate paper to gen…
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…