2 citations · 2 across the 7 of their papers we have counts for
7 papers
Extinction and propagation phenomena for semilinear parabolic equations on metric trees
Fabio Punzo, Alberto Tesei
We study the Cauchy-Neumann problem on a regular metric tree T for the semilinear heat equation with forcing term of KPP type. Propagation and extinction of solutions, as well as a…
Monotonicity results for semilinear parabolic equations on metric graphs
Fabio Punzo, Alberto Tesei
We prove monotonicity results for semilinear parabolic problems on locally finite connected metric graphs. Applications to regular metric trees are discussed.
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…