Related papers: On the stochastic Cahn-Hilliard equation with a si…
We study the Cahn-Hilliard equation with non-degenerate concentration-dependent mobility and logarithmic potential in two dimensions. We show that any weak solution is unique, exhibits propagation of uniform-in-time regularity, and…
We study the sharp interface limit of the stochastic Cahn-Hilliard equation with cubic double-well potential and additive space-time white noise $\epsilon^{\sigma}\dot{W}$ where $\epsilon>0$ is an interfacial width parameter. We prove that,…
In this paper, we investigate a rather general system of two operator equations that has the structure of a viscous or nonviscous Cahn--Hilliard system in which nonlinearities of double-well type occur. Standard cases like regular or…
We show existence and pathwise uniqueness of probabilistically strong solutions to a pseudomonotone stochastic evolution problem on a bounded domain $D\subseteq\mathbb{R}^d$, $d\in\mathbb{N}$, with homogeneous Dirichlet boundary conditions…
We study positive solutions of semilinear elliptic equations in a planar triangular domain under mixed boundary conditions, consisting of homogeneous Dirichlet boundary conditions on one side and homogeneous Neumann boundary conditions on…
We consider a class of Cahn-Hilliard equation that models phase separation process of binary mixtures involving nontrivial boundary interactions in a bounded domain with non-permeable wall. The system is characterized by certain dynamic…
We consider the stationary Boltzmann equation with the angular cutoff cross section in a bounded convex domain under the incoming boundary condition. In this article, we discuss the fractional Sobolev regularity of the solution without…
We study a general Navier-Stokes-Cahn-Hilliard-Boussinesq system that describes the motion of a mixture of two incompressible Newtonian fluids with thermo-induced Marangoni effects. The Cahn-Hilliard dynamics of the binary mixture is…
In this paper, we investigate the problems of Cauchy theory and exponential stability for the inhomogeneous Boltzmann equation without angular cut-off. We only deal with the physical case of hard potentials type interactions (with a…
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 the randomness appearing at the…
We consider a stochastic partial differential equation with a logarithmic nonlinearity with singularities at $1$ and $-1$ and a constraint of conservation of the space average. The equation, driven by a trace-class space-time noise,…
We prove global existence and uniqueness of solutions to a Cahn-Hilliard system with nonlinear viscosity terms and nonlinear dynamic boundary conditions. The problem is highly nonlinear, characterized by four nonlinearities and two separate…
In this paper we are concerned with the homogenization property of stochastic non-homogeneous incompressible Navier-Stokes equations with rapid oscillation in a smooth bounded domain of $\mathbb{R}^d$, $d=2,3$, and driven by multiplicative…
The existence of global martingale weak solution for the 2D and 3D stochastic Cahn-Hilliard-Navier-Stokes equations driven by multiplicative noise in a smooth bounded domain is established. In particular, the system is supplied with the…
In this paper, we characterize the topological support in Holder norm of the law of the solution to a stochastic wave equation with three-dimensional space variable is proved. This note is a continuation of [9] and [10]. The result is a…
In the present contribution we study a viscous Cahn-Hilliard system where a further leading term in the expression for the chemical potential $ \mu$ is present. This term consists of a subdifferential operator $S$ in $L^2(\Omega)$ (where…
We consider Hamilton-Jacobi equations in one space dimension with Hamiltonians of the form $H(p,x,\omega) = G(p) + \beta V(x,\omega)$, where $V(\cdot,\omega)$ is a stationary and ergodic potential of unit amplitude. The homogenization of…
We consider the 2-dimensional spatially homogeneous Boltzmann equation for hard potentials. We assume that the initial condition is a probability measure that has some exponential moments and is not a Dirac mass. We prove some…
We study singular limits of stochastic evolution equations in the interplay of disappearing strength of the noise and insufficient regularity, where the equation in the limit with noise would not be defined due to lack of regularity. We…
In a Hilbert space setting, we study the stability properties of the regularized continuous Newton method with two potentials, which aims at solving inclusions governed by structured monotone operators. The Levenberg-Marquardt…