Related papers: Global martingale solutions for a stochastic popul…
An implicit Euler finite-volume scheme for a nonlocal cross-diffusion system on the multidimensional torus is analyzed. The equations describe the dynamics of population species with repulsive or attractive interactions. The numerical…
We discuss the global existence of solutions to a system of stochastic Schr\"odinger equations with multiplicative noise. Our setting of the quadratic nonlinear terms in dimension 4 is $L^2$-critical. We treat the solutions under the ground…
We consider reaction-diffusion systems where components diffuse inside the domain and react on the surface through mass transport type boundary conditions on an evolving domain. Using Lyapunov functional and duality arguments, we establish…
In this paper, we consider the numerical solution of the one-dimensional Schr\"odinger equation with a periodic lattice potential and a random external potential. This is an important model in solid state physics where the randomness is…
In this work, we investigate the dynamics of an inhomogeneous coupled nonlinear Schrodinger system with quadratic-type interactions. Such systems arise naturally in nonlinear dynamics and mathematical physics, particularly in nonlinear…
In this paper, we investigate a Stokes-Magneto system with fractional diffusions. We first deal with the non-resistive case in $\mathbb{T}^{d}$ and establish the local and global well-posedness with initial magnetic field $\mathbf{b}_0\in…
We establish the existence of solutions to a class of non-linear stochastic differential equation of reaction-diffusion type in an infinite-dimensional space, with diffusion corresponding to a given transition kernel. The solution obtained…
This paper deals with the existence of global weak solutions for a wide class of (multiple species) cross-diffusions systems. The existence is based on two different ingredients: an entropy estimate giving some gradient control and a…
We formulate a dynamical fluctuation theory for stationary non equilibrium states (SNS) which is tested explicitly in stochastic models of interacting particles. In our theory a crucial role is played by the time reversed dynamics. Within…
We investigate numerical behaviour of a convection diffusion equation with random coefficients by approximating statistical moments of the solution. Stochastic Galerkin approach, turning the original stochastic problem to a system of…
Existence of nontrivial nonnegative equilibrium solutions for age structured population models with nonlinear diffusion is investigated. Introducing a parameter measuring the intensity of the fertility, global bifurcation is shown of a…
Although diffusion models have successfully extended to function-valued data, stochastic interpolants -- which offer a flexible way to bridge arbitrary distributions -- remain limited to finite-dimensional settings. This work bridges this…
Nonlinear Fokker-Planck equations play a major role in modeling large systems of interacting particles with a proved effectiveness in describing real world phenomena ranging from classical fields such as fluids and plasma to social and…
This paper is devoted to the construction of structure preserving stochastic Galerkin schemes for Fokker-Planck type equations with uncertainties and interacting with an external distribution, that we refer to as a background distribution.…
We study the stochastic nonlinear Schroedinger equations with linear multiplicative noise, particularly in the defocusing mass-critical and energy-critical cases. For general initial data, we prove the global existence and uniqueness of…
In this paper the author reviews a version of the global Galerkin that was developed and applied in a series of earlier publications. The method is based on divergence-free basis functions satisfying all the linear and homogeneous boundary…
We consider a nonlinear stochastic partial differential equation (SPDE) that takes the form of the Camassa--Holm equation perturbed by a convective, position-dependent, noise term. We establish the first global-in-time existence result for…
We show the existence of local and global in time weak martingale solutions for a stochastic version of the Othmer-Dunbar-Alt kinetic model of chemotaxis under suitable assumptions on the turning kernel and stochastic drift coefficients,…
Wave propagation problems for heterogeneous media are known to have many applications in physics and engineering. Recently, there has been an increasing interest in stochastic effects due to the uncertainty, which may arise from impurities…
It is well-established that including spatial structure and stochastic noise in models for predator-prey interactions invalidates the classical deterministic Lotka-Volterra picture of neutral population cycles. In contrast, stochastic…