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In this paper we initiate the mathematical analysis of a system of nonlinear Stochastic Partial Differential equations describing the motion of turbulent Non-Newtonian media in the presence of fluctuating magnetic field. The system is…
In this paper we study a nonlinear stochastic fluid-structure interaction problem with a multiplicative, white-in-time noise. The problem consists of the Navier-Stokes equations describing the flow of an incompressible, viscous fluid in a…
In this paper, we consider a class of slow-fast systems of stochastic partial differential equations where the nonlinearity in the slow equation is not continuous and unbounded. We first provide conditions that ensure the existence of a…
In this paper, we study the classical Keller - Segel system on a two-dimensional domain perturbed by a pair of Wiener processes, where the leading diffusion term is replaced by a porous media term. Since the randomness is intrinsic, the…
We consider Lie and Strang splitting for the time integration of constrained partial differential equations with a nonlinear reaction term. Since such systems are known to be sensitive with respect to perturbations, the splitting procedure…
We show a stochastic version of the Schauder-Tychonoff fixed point theorem which yields a solution of the martingale problem for a class of systems of nonlinear reaction-diffusion equations driven by a cylindrical Wiener process and a…
In this paper, we study the stochastic degenerate Keller-Segel system perturbed by linear multiplicative noise in a bounded domain $\mathcal{O}$. We establish the global existence of martingale solutions for this model with any nonnegative…
The construction of stochastic solutions for nonlinear partial differential equations is a powerful method to obtain new exact results and to develop efficient numerical algorithms, in particular when domain decomposition techniques are…
A coupled system of nonlinear mixed-type equations modeling early stages of angiogenesis is analyzed in a bounded domain. The system consists of stochastic differential equations describing the movement of the positions of the tip and stalk…
We construct non-negative martingale solutions to the stochastic porous medium equation in one dimension with homogeneous Dirichlet boundary conditions which exhibit a type of sticky behavior at zero. The construction uses the stochastic…
On the one hand, we investigate the existence and pathwise uniqueness of a nonnegative martingale solution to the stochastic evolution system of nonlinear advection-diffusion equations proposed by Klausmeier with Gaussian multiplicative…
The global weak martingale solution is built through a four-level approximation scheme to stochastic compressible active liquid crystal system driven by multiplicative noise in a smooth bounded domain in $\mathbb{R}^{3}$ with large initial…
In this paper we develop non-stationary martingale techniques for dependent data. We shall stress the non-stationary version of the projective Maxwell-Woodroofe condition, which will be essential for obtaining maximal inequalities and…
We consider a system of reaction-diffusion equations including chemotaxis terms and coming out of the modeling of multiple sclerosis. The global existence of strong solutions to this system in any dimension is proved, and it is also shown…
The macroscopic behavior of the solution of a coupled system of partial differential equations arising in the modeling of reaction-diffusion processes in periodic porous media is analyzed. Our mathematical model can be used for studying…
This paper presents the first in a series of results that allow us to develop a theory providing finer control over the complexity of normalisation, and in particular of cut elimination. By considering atoms as self-dual non-commutative…
In this paper, we develop necessary and sufficient conditions for the validity of a martingale approximation for the partial sums of a stationary process in terms of the maximum of consecutive errors. Such an approximation is useful for…
A decomposition principle for nonlinear dynamic compartmental systems is introduced in the present paper. This theory is based on the mutually exclusive and exhaustive, analytical and dynamic, novel system and subsystem partitioning…
In this paper, we extend the results of Elliott and Yang \cite{elliott3} and discuss the control of a stochastic process for which the driving noise is provided by a martingale associated with a semi-Markov Chain. An existence and a…
In this paper by exploiting critical point theory, the existence of two distinct nontrivial solutions for a nonlinear algebraic system with a parameter is established. Our goal is achieved by requiring an appropriate behavior of the…