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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…
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 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…