Singular stochastic Allen–Cahn equations with dynamic boundary conditions

@article{Orrieri2019SingularSA,
  title={Singular stochastic Allen–Cahn equations with dynamic boundary conditions},
  author={Carlo Orrieri and Luca Scarpa},
  journal={Journal of Differential Equations},
  year={2019}
}
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16 Citations
Background Citations
8
Methods Citations
5

16 Citations

Stochastic Allen–Cahn equation with logarithmic potential
On the stochastic Cahn–Hilliard equation with a singular double-well potential
A stochastic Allen-Cahn-Navier-Stokes system with singular potential
. 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–Stokes equation…
The Stochastic Viscous Cahn–Hilliard Equation: Well-Posedness, Regularity and Vanishing Viscosity Limit
  • Luca Scarpa
  • Mathematics
    Applied Mathematics & Optimization
  • 2020
Well-posedness is proved for the stochastic viscous Cahn–Hilliard equation with homogeneous Neumann boundary conditions and Wiener multiplicative noise. The double-well potential is allowed to have…
The Cahn-Hilliard Equation with Forward-Backward Dynamic Boundary Condition via Vanishing Viscosity
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 phase variable tends to…
A variational approach to some classes of singular stochastic PDEs
This thesis contains an analysis of certain classes of parabolic stochastic partial differential equations with singular drift and multiplicative Wiener noise. Equations of this type have been…
Random separation property for stochastic Allen-Cahn-type equations
We study a large class of stochastic p-Laplace Allen-Cahn equations with singular potential. Under suitable assumptions on the (multiplicative-type) noise we first prove existence, uniqueness, and…
The stochastic Cahn–Hilliard equation with degenerate mobility and logarithmic potential
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 logarithmic or…
Analysis and Optimal Velocity Control of a Stochastic Convective Cahn–Hilliard Equation
A Cahn–Hilliard equation with stochastic multiplicative noise and a random convection term is considered. The model describes isothermal phase-separation occurring in a moving fluid, and accounts for…
Degenerate Kolmogorov equations and ergodicity for the stochastic Allen-Cahn equation with logarithmic potential
Well-posedness à la Friedrichs is proved for a class of degenerate Kolmogorov equations associated to stochastic Allen-Cahn equations with logarithmic potential. The thermodynamical consistency of…
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References

SHOWING 1-10 OF 40 REFERENCES
Global solution to the Allen–Cahn equation with singular potentials and dynamic boundary conditions
On the stochastic Cahn–Hilliard equation with a singular double-well potential
A variational approach to dissipative SPDEs with singular drift
We prove global well-posedness for a class of dissipative semilinear stochastic evolution equations with singular drift and multiplicative Wiener noise. In particular, the nonlinear term in the drift…
The non-isothermal Allen-Cahn equation with dynamic boundary conditions
We consider a model of nonisothermal phase transitions taking place in a bounded spatial region. The order parameter $\psi$ is governed by an Allen-Cahn type equation which is coupled with the…
Well-posedness for a class of doubly nonlinear stochastic PDEs of divergence type
Optimal Control of an Allen-Cahn Equation with Singular Potentials and Dynamic Boundary Condition
TLDR
This paper first extends known well-posedness and regularity results for the state equation and then shows the existence of optimal controls and that the control-to-state mapping is twice continuously Fr\'echet differentiable between appropriate function spaces, and establishes first-order necessary optimality conditions.
Strong solutions to SPDEs with monotone drift in divergence form
We prove existence and uniqueness of strong solutions, as well as continuous dependence on the initial datum, for a class of fully nonlinear second-order stochastic PDEs with drift in divergence…
Strong Solutions for Stochastic Partial Differential Equations of Gradient Type
A variational approach to stochastic nonlinear diffusion problems with dynamical boundary conditions
We study a nonlinear partial differential equation of the calculus of variation in a bounded domain, perturbed by noise; we allow stochastic boundary conditions that depend on the time derivative of…
ON THE ASYMPTOTIC BEHAVIOR OF THE CAGINALP SYSTEM WITH DYNAMIC BOUNDARY CONDITIONS
We consider a phase-field system of Caginalp type on a three-dimensional bounded domain. The order parameter $\psi $ fulfills a dynamic boundary condition, while the (relative) temperature $\theta…
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