7 citations · 9 across the 5 of their papers we have counts for
5 papers
On the evolution of subcritical regions for the Perona-Malik equation
Marina Ghisi, Massimo Gobbino
The Perona-Malik equation is a celebrated example of forward-backward parabolic equation. The forward behavior takes place in the so-called subcritical region, in which the gradien…
An example of global classical solution for the Perona-Malik equation
Marina Ghisi, Massimo Gobbino
We consider the Cauchy problem for the Perona-Malik equation in an open subset of R^{n}, with Neumann boundary conditions. It is well known that in the one-dimensional case this pr…
Mildly degenerate Kirchhoff equations with weak dissipation: global existence and time decay
Marina Ghisi, Massimo Gobbino
We consider the hyperbolic-parabolic singular perturbation problem for a degenerate quasilinear Kirchhoff equation with weak dissipation. This means that the coefficient of the dis…
Hyperbolic--parabolic singular perturbation for nondegenerate Kirchhoff equations with critical weak dissipation
Marina Ghisi, Massimo Gobbino
We consider the hyperbolic-parabolic singular perturbation problem for a nondegenerate quasilinear equation of Kirchhoff type with weak dissipation. This means that the dissipative…
Derivative loss for Kirchhoff equations with non-Lipschitz nonlinear term
Marina Ghisi, Massimo Gobbino
In this paper we consider the Cauchy boundary value problem for the abstract Kirchhoff equation with a continuous nonlinearity m : [0,+\infty) --> [0,+\infty). It is well known tha…