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Local asymptotics for the nonlocal Swift-Hohenberg equation
Elisa Davoli, Christian Kuehn, Luca Scarpa +1
The nonlocal-to-local asymptotics investigation for evolutionary problems is a central topic both in the theory of PDEs and in functional analysis. More recently, it became the mai…
Local asymptotics and optimal control for a viscous Cahn-Hilliard-Reaction-Diffusion model for tumor growth
Elisa Davoli, Elisabetta Rocca, Luca Scarpa +1
In this paper we study nonlocal-to-local asymptotics for a tumor-growth model coupling a viscous Cahn-Hilliard equation describing the tumor proportion with a reaction-diffusion eq…
Nonlocal-to-local convergence of Cahn-Hilliard equations: Neumann boundary conditions and viscosity terms
Elisa Davoli, Luca Scarpa, Lara Trussardi
We consider a class of nonlocal viscous Cahn-Hilliard equations with Neumann boundary conditions for the chemical potential. The double-well potential is allowed to be singular (e.…
Degenerate nonlocal Cahn-Hilliard equations: well-posedness, regularity and local asymptotics
Elisa Davoli, Helene Ranetbauer, Luca Scarpa +1
Existence and uniqueness of solutions for nonlocal Cahn-Hilliard equations with degenerate potential is shown. The nonlocality is described by means of a symmetric singular kernel…
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…