Searcharxiv⌕ Search

arXiv subjects

Ioana Ciotir

Publications and source records attributed to Ioana Ciotir.

At least 19 recordsLinked to original sources
arXiv2026

The vanishing latent heat limit of a stochastic Stefan problem : An error estimate

The purpose of this paper is to extend an article by Hilhorst, Mimura and Sch{ä}tzle [18] about the limit as the latent heat coefficient tends to zero of a two-phase Stefan problem arising in biology. We introduce a rather general additive noise white in time and colored in space, and search for the limit of the solution of the corresponding stochastic Stefan problem as the latent heat coefficient vanishes. We first prove the existence and uniqueness of the weak solution of this problem, and then study the limit of the solution as the latent heat coefficient tends to zero. Unlike in [18], our method of proof is based upon an error estimate between the solution of the Stefan problem with positive latent heat and that of the Stefan problem with zero latent heat, which seems to be novel even in the deterministic case when no noise is added.

math.AP↗
arXiv2026

Stochastic Control of Addiction with State-Dependent Jump Relapse

We study a continuous-time rational addiction model where addiction capital follows a piecewise deterministic Markov process with state-dependent jumps capturing relapse and recovery. The instantaneous utility combines consumption and addiction capital via a power specification, leading to Hamilton-Jacobi-Bellman (HJB) equations with nonlocal jump terms. In the capped, bounded-control case we obtain a unique bounded viscosity solution and prove that optimal policies are bang-bang, switching between minimal and maximal consumption, while in the uncapped case we derive explicit linear feedback controls and closed-form value functions in several parameter regimes.

math.OC↗
arXiv2025

Optimality Conditions for Control Systems Governed by Monotone Stochastic Evolution Equations

We study a class of optimal control problems governed by nonlinear stochastic equations of monotone type under certain coercivity and linear growth conditions. We give first order necessary conditions of optimality. A stochastic Pontryagin principle can be recovered in the case that the diffusion doesn't depend on the control. We give several applications, most notably for stochastic porous media equations in the Lipschitz case.

math.OC↗
arXiv2025

Stochastic evolution equations with nonlinear diffusivity, recent progress and critical cases

This short survey article stems from recent progress on critical cases of stochastic evolution equations in variational formulation with additive, multiplicative or gradient noises. Typical examples appear as the limit cases of the stochastic porous medium equation, stochastic fast- and super fast-diffusion equations, self-organized criticality, stochastic singular $p$-Laplace equations, and the stochastic total variation flow, among others. We present several different notions of solutions, results on convergence of solutions depending on a parameter, and homogenization. Furthermore, we provide some references hinting at the recent progress in regularity results, long-time behavior, ergodicity, and numerical analysis.

math.PR↗
arXiv2025

The Stefan problem with mushy region as a scaling limit of stochastic PDE with turbulent transport

This work establishes a scaling limit theorem for the Stefan problem incorporating a mushy region, demonstrating that solutions to stochastic variants with turbulent transport terms converge to the solution to a deterministic partial differential equation. The analysis builds upon recent advances in stochastic phase-change modeling and turbulent flow mathematics in [5]. In the physical interpretation of an ice melting process, our result shows that turbulence accelerates ice melting.

math.AP↗
arXiv2025

An Existence Result for a Stochastic Stefan Problem With Mushy Region and Turbulent Transport Noise

This work is devoted to the proof of the existence of a martingale solution for a complex version of the stochastic Stefan problem. This particular formulation incorporates two important features: a mushy region and turbulent transport within the liquid phase. While our approach bears similarities to porous media equations, it differs in a crucial aspect. Instead of using the typical framework for such equations, we have chosen to work within an L2 space. This choice is motivated by the nature of the operator that characterizes the turbulent noise in our model. The L2 space provides a more natural and appropriate setting for handling this specific operator, allowing us to better capture and analyze the turbulent transport phenomena in the liquid phase of the Stefan problem.

math.AP↗
arXiv2024

A Stochastic Porous Media Schr{ö}dinger Equation: Feynman-type Motivation, Well-Posedness and Control Interpretation

This paper's aim is threefold. First, using Feynman's path approach to the derivation of theclassical Schr{ö}dinger's equation in [6] and by introducing a slight path (or wave) dependency ofthe action, we derive a new class of equations of Schr{ö}dinger type where the driving operatoris no longer the Laplace one but rather of complex porous media-type. Second, using suitableconcepts of monotonicity in the complex setting and on appropriate functional spaces, we showthe existence and uniqueness of the solution to this type of equation. In the formulation of ourequation, we adjoin possible measurement absolute errors translating in an additive Brownianperturbation and interactions between different waves translating in a mean-field (or McKean-Vlasov) dependency of drift coefficient. Finally, using Fitzpatrick's characterization of maximalmonotone operators (cf. [7]), we propose a Br{é}zis-Ekeland type characterization of the solutionof the deterministic equation via a control problem. This is envisaged as a possible way toovercome strict monotonicity requirements in the complex setting.

math.AP↗
arXiv2024

Stochastic porous media equation with Robin boundary conditions, gravity-driven infiltration and multiplicative noise

We aim at studying a novel mathematical model associated to a physical phenomenon of infiltration in an homogeneous porous medium. The particularities of our system are connected to the presence of a gravitational acceleration term proportional to the level of saturation, and of a Brownian multiplicative perturbation. Furthermore, the boundary conditions intervene in a Robin manner with the distinction of the behavior along the inflow and outflow respectively. We provide qualitative results of well-posedness, the investigation being conducted through a functional approach.

math.AP↗
arXiv2023

Improved regularity for the stochastic fast diffusion equation

We prove that the solution to the singular-degenerate stochastic fast-diffusion equation with parameter $m\in (0,1)$, with zero Dirichlet boundary conditions on a bounded domain in any spatial dimension, and driven by linear multiplicative Wiener noise, exhibits improved regularity in the Sobolev space $W^{1,m+1}_0$ for initial data in $L^{2}$.

math.AP↗
arXiv2023

The stochastic fast logarithmic equation in $\mathbb{R}^{d}$ with multiplicative Stratonovich noise

This paper is concerned with the existence and uniqueness of the solution for the stochastic fast logarithmic equation with Stratonovich multiplicative noise in $\mathbb{R}^{d}$ for $d\geqslant 3$. It provides an answer to a critical case (morally speaking, corresponding to the porous media operator $ΔX^m$ for $m=0$) left as an open problem in the paper Barbu-Röckner-Russo (Journal de Mathématiques Pures et Appliquées,103(4):1024--1052, 2015). We face several technical difficulties related both to the degeneracy properties of the logarithm and to the fact that the problem is treated in an unbounded domain. Firstly, the order in which the approximations are considered is very important and different from previous methods. Secondly, the energy estimates needed in the last step can only be achieved with a well-chosen Stratonovich-type rectification of the noise.

math.PR↗
arXiv2022

Asymptotic issue for porous media systems with linear multiplicative gradient-type noise via state constrained arguments

The aim of the present paper is to provide necessary and sufficient conditions to maintain a stochastic coupled system, with porous media components and gradient-type noise in a prescribed set of constraints by using internal controls. This work is a continuation of the results in [10], as we consider the case of divergence type noise perturbation. On the other hand, it provides a different framework in which the quasi-tangency condition can be obtained with optimal speed. In comparison with the aforementioned result, here we transform the stochastic system into a random deterministic one, via the rescaling approach, then we study the viability of random sets. As an application, conditions for the stabilization of the stochastic porous media equations are obtained.

math.AP↗
arXiv2022

State-constrained porous media control systems with application to stabilization

We aim at providing a characterization of the ability to maintain a stochastic coupled system with porous media components in a prescribed set of constraints by using internal controls. This property is proven via a quasi-tangency local-in-time condition in the spirit of Euler approximation schemes. In particular, by employing one of the components of the system as asymptotic supervisor, we give conditions guaranteeing the exponential asymptotic stabilizability of controlled porous media equations.

math.OC↗
arXiv2016

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

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, Brzeźniak, Hausenblas, Tubaro; Stoch. Proc. Appl., 123 (2013)] and [Barbu, Röckner; J. Eur. Math. Soc., 17 (2015)].

math.AP↗
arXiv2015

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.

math.PR↗
arXiv2013

Probabilistic representation for solutions of a porous media type equation with Neumann boundary condition: the case of the half-line

The purpose of this paper consists in proposing a generalized solution for a porous media type equation on a half-line with Neumann boundary condition and prove a probabilistic representation of this solution in terms of an associated microscopic diffusion. The main idea is to construct a stochastic differential equation with reflection which has a solution in law and whose marginal law densities provide the unique solution of the porous media type equation.

math.PR↗
arXiv2012

Convergence of invariant measures for singular stochastic diffusion equations

It is proved that the solutions to the singular stochastic $p$-Laplace equation, $p\in (1,2)$ and the solutions to the stochastic fast diffusion equation with nonlinearity parameter $r\in (0,1)$ on a bounded open domain $Λ\subset\R^d$ with Dirichlet boundary conditions are continuous in mean, uniformly in time, with respect to the parameters $p$ and $r$ respectively (in the Hilbert spaces $L^2(Λ)$, $H^{-1}(Λ)$ respectively). The highly singular limit case $p=1$ is treated with the help of stochastic evolution variational inequalities, where $\mathbbm{P}$-a.s. convergence, uniformly in time, is established. It is shown that the associated unique invariant measures of the ergodic semigroups converge in the weak sense (of probability measures).

math.PR↗
arXiv2011

Existence and uniqueness of solution for the stochastic nonlinear diffusion equation of plasma

In this paper we are concerned with the stochastic partial differential equations of super-fast diffusion processes describing behavior of plasma dX(t)-Δln(X(t)+1)dt=\surd(Q)dW(t), in (0,T)\timesO, where O is a bounded open subset of R. We define a strong solution adequate to the properties of the natural logarithm and we prove the corresponding existence and uniqueness result.

math.PR↗