16 citations · 39 across the 7 of their papers we have counts for
8 papers
From nonlocal to local Cahn-Hilliard equation
Stefano Melchionna, Helene Ranetbauer, Luca Scarpa +1
In this paper we prove the convergence of a nonlocal version of the Cahn-Hilliard equation to its local counterpart as the nonlocal convolution kernel is scaled using suitable appr…
Porous medium equation with a blow-up nonlinearity and a non-decreasing constraint
Goro Akagi, Stefano Melchionna
The final goal of this paper is to prove existence of local (strong) solutions to a (fully nonlinear) porous medium equation with blow-up term and nondecreasing constraint. To this…
Long-time behavior of a nonlocal Cahn-Hilliard equation with reaction
Annalisa Iuorio, Stefano Melchionna
In this paper we study the long-time behavior of a nonlocal Cahn-Hilliard system with singular potential, degenerate mobility, and a reaction term. In particular, we prove the exis…
Elliptic-regularization of nonpotential perturbations of doubly-nonlinear gradient flows of nonconvex energies: A variational approach
Goro Akagi, Stefano Melchionna
This paper presents a variational approach to doubly-nonlinear (gradient) flows (P) of nonconvex energies along with nonpotential perturbations (i.e., perturbation terms without an…
A variational approach to symmetry, monotonicity, and comparison for doubly-nonlinear equations
Stefano Melchionna
We advance a variational method to prove qualitative properties such as symmetries, monotonicity, upper and lower bounds, sign properties, and comparison principles for a large cla…
Varifold solutions of a sharp interface limit of a diffuse interface model for tumor growth
S. Melchionna, E. Rocca
We discuss the sharp interface limit of a diffuse interface model for a coupled Cahn-Hilliard--Darcy system that models tumor growth when a certain parameter , relat…
A variational principle for nonpotential perturbations of gradient flows of nonconvex energies
Stefano Melchionna
We investigate a variational approach to nonpotential perturbations of gradient flows of nonconvex energies in Hilbert spaces. We prove existence of solutions to elliptic-in-time r…
On a nonlocal Cahn-Hilliard equation with a reaction term
Stefano Melchionna, Elisabetta Rocca
We prove existence, uniqueness, regularity and separation properties for a nonlocal Cahn-Hilliard equation with a reaction term. We deal here with the case of logarithmic potential…