Ioana Ciotir

Convergence of invariant measures for singular stochastic diffusion equations

It is proved that the solutions to the singular stochastic p-Laplace equation, p∈(1,2) and the solutions to the stochastic fast diffusion equation with nonlinearity parameter r∈(0,1) on a bounded open domain Λ⊂Rd with Dirichlet boundary conditions are continuous in mean, uniformly in time, with respect to the parameters p and r respectively (in the Hilbert spaces L2(Λ), H−1(Λ) respectively). The highly singular limit case p=1 is treated with the help of stochastic evolution variational inequalities, where P-a.s. convergence, uniformly in time, is established.

Nonlinear stochastic partial differential equations with singular diffusivity and gradient Stratonovich noise

Abstract We study existence and uniqueness of a variational solution in terms of stochastic variational inequalities (SVI) to stochastic nonlinear diffusion equations with a highly singular diffusivity term and multiplicative Stratonovich gradient-type noise. We derive a commutator relation for the unbounded noise coefficients in terms of a geometric Killing vector condition. The drift term is given by the total variation flow, respectively, by a singular p -Laplace-type operator. We impose nonlinear zero Neumann boundary conditions and precisely investigate their connection with the coefficient fields of the noise. This solves an open problem posed in Barbu et al. (2013) [7] and Barbu and Rockner (2015) [10] .

Corrigendum to “Convergence of invariant measures for singular stochastic diffusion equations” [Stochastic Process. Appl. 122 (2012) 1998–2017]

Abstract We correct a few errors that appeared in [Convergence of invariant measures for singular stochastic diffusion equations, Stochastic Process. Appl. 122 (4) (2012) 1998–2017] by I. Ciotir and J.M. Tolle.

Self-repelling diffusions via an infinite dimensional approach

In the present work we study self-interacting diffusions following an infinite dimensional approach. First we prove existence and uniqueness of a solution with Markov property. Then we study the corresponding transition semigroup and, more precisely, we prove that it has Feller property and we give an explicit form of an invariant probability of the system.

A Variational Approach to Neumann Stochastic Semi-Linear Equations Modeling the Thermostatic Control

In the present paper, we prove existence and uniqueness of a mild solution for a stochastic semi-linear equation with Neumann boundary conditions, using only general monotonicity assumptions. The study of this equation is motivated by physical applications as the model of the temperature control through the boundary. The result is proved by using an optimal control approach based on the variational principle of Brezis and Ekeland.