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A stochastic Allen-Cahn-Navier-Stokes system with singular potential
Andrea Di Primio, Maurizio Grasselli, Luca Scarpa
We investigate a stochastic version of the Allen-Cahn-Navier-Stokes system in a smooth two- or three-dimensional domain with random initial data. The system consists of a Navier-St…
The Energy-Dissipation Principle for stochastic parabolic equations
Luca Scarpa, Ulisse Stefanelli
The Energy-Dissipation Principle provides a variational tool for the analysis of parabolic evolution problems: solutions are characterized as so-called null-minimizers of a global…
The Cahn-Hilliard equation with forward-backward dynamic boundary condition via vanishing viscosity
Pierluigi Colli, Takeshi Fukao, Luca Scarpa
An asymptotic analysis for a system with equation and dynamic boundary condition of Cahn-Hilliard type is carried out as the coefficient of the surface diffusion acting on the phas…
An extended variational theory for nonlinear evolution equations via modular spaces
Alexander Menovschikov, Anastasia Molchanova, Luca Scarpa
We propose an extension of the classical variational theory of evolution equations that accounts for dynamics also in possibly non-reflexive and non-separable spaces. The pivoting…
Parameter identification for nonlocal phase field models for tumor growth via optimal control and asymptotic analysis
Elisabetta Rocca, Luca Scarpa, Andrea Signori
We introduce the problem of parameter identification for a coupled nonlocal Cahn-Hilliard-reaction-diffusion PDE system stemming from a recently introduced tumor growth model. The…
Doubly nonlinear stochastic evolution equations II
Luca Scarpa, Ulisse Stefanelli
Complementing the analysis in [41], we investigate the well-posedness of SPDEs problems of doubly nonlinear type. These arise ubiquitously in the modelization of dissipative media…