40 citations · 405 across the 53 of their papers we have counts for
9 papers · 1 filter
On the positivity of local mild solutions to stochastic evolution equations
Carlo Marinelli, Luca Scarpa
We provide sufficient conditions on the coefficients of a stochastic evolution equation on a Hilbert space of functions driven by a cylindrical Wiener process ensuring that its mil…
Local asymptotics for nonlocal convective Cahn-Hilliard equations with W^{1,1} kernel and singular potential
Elisa Davoli, Luca Scarpa, Lara Trussardi
We prove existence of solutions and study the nonlocal-to-local asymptotics for nonlocal, convective, Cahn-Hilliard equations in the case of a W^{1,1} convolution kernel and under…
An order approach to SPDEs with antimonotone terms
Luca Scarpa, Ulisse Stefanelli
We consider a class of parabolic stochastic partial differential equations featuring an antimonotone nonlinearity. The existence of unique maximal and minimal variational solutions…
The stochastic Cahn-Hilliard equation with degenerate mobility and logarithmic potential
Luca Scarpa
We prove existence of martingale solutions for the stochastic Cahn-Hilliard equation with degenerate mobility and multiplicative Wiener noise. The potential is allowed to be of log…
Bounded solutions and their asymptotics for a doubly nonlinear Cahn-Hilliard system
Elena Bonetti, Pierluigi Colli, Luca Scarpa +1
In this paper we deal with a doubly nonlinear Cahn-Hilliard system, where both an internal constraint on the time derivative of the concentration and a potential for the concentrat…
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.…
Optimal control of stochastic phase-field models related to tumor growth
Carlo Orrieri, Elisabetta Rocca, Luca Scarpa
We study a stochastic phase-field model for tumor growth dynamics coupling a stochastic Cahn-Hilliard equation for the tumor phase parameter with a stochastic reaction-diffusion eq…
Doubly nonlinear stochastic evolution equations
Luca Scarpa, Ulisse Stefanelli
We present an existence theory for martingale and strong solutions to doubly nonlinear evolution equations in a separable Hilbert space in the form $$d(Au) + Bu\,dt \ni F(u)\,dt +…
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…