5 papers
Discontinuous solutions of Hamilton-Jacobi equations versus Radon measure-valued solutions of scalar conservation laws: Disappearance of singularities
M. Bertsch, F. Smarrazzo, A. Terracina +1
Let be a bounded and Lipschitz continuous function. We consider discontinuous viscosity solutions of the Hamilton-Jacobi equation and signed Radon measure valu…
Signed Radon measure-valued solutions of flux saturated scalar conservation laws
M. Bertsch, F. Smarrazzo, A. Terracina +1
We prove existence and uniqueness for a class of signed Radon measure-valued entropy solutions of the Cauchy problem for a first order scalar hyperbolic conservation law in one spa…
Discontinuous viscosity solutions of first order Hamilton-Jacobi equations
M. Bertsch, F. Smarrazzo, A. Terracina +1
We consider the simplest example of a time-dependent first order Hamilton-Jacobi equation, in one space dimension and with a bounded and Lipschitz continuous Hamiltonian which only…
A uniqueness criterion for measure-valued solutions of scalar hyperbolic conservation laws
Michiel Bertsch, Flavia Smarrazzo, Andrea Terracina +1
We prove existence and uniqueness of Radon measure-valued solutions of the Cauchy problem $$ \begin{cases} u_t+[φ(u)]_x=0 & \text{in } \mathbb{R}\times (0,T) \\ u=u_0\ge 0 &\text{i…
Radon measure-valued solutions of first order hyperbolic conservation laws
Michiel Bertsch, Flavia Smarrazzo, Andrea Terracina +1
We study nonnegative solutions of the Cauchy problem $$ \begin{cases} u_t+[φ(u)]_x=0 & \text{in } \mathbb{R}\times (0,T) \\ u=u_0\ge 0&\text{in } \mathbb{R}\times \{0\}, \end{cases…