Related papers: Weak universality for a class of 3d stochastic rea…
In this work, we study the global existence of solutions for a class of semilinear nonlocal reaction-diffusion systems with $m$ components on a bounded domain $\Omega$ in $\mathbb{R}^n$ with smooth boundary. The initial data is assumed to…
We study a system of nonlinear partial differential equations describing the unsteady motions of incompressible chemically reacting non-Newtonian fluids. The system under consideration consists of the generalized Navier-Stokes equations…
We investigate the existence of weak solutions to a multi-component system, consisting of compressible chemically reacting components, coupled with the compressible Stokes equation for the velocity. Specifically, we consider the case of…
We investigate a class of three-component reaction-diffusion systems subject to mass control and a newly introduced structural assumption, referred to as linear intermediate weighted sum condition. Under these hypotheses, we establish the…
The global existence of bounded weak solutions to a diffusion system modeling biofilm growth is proven. The equations consist of a reaction-diffusion equation for the substrate concentration and a fourth-order Cahn-Hilliard-type equation…
A class of parabolic cross-diffusion systems modeling the interaction of an arbitrary number of population species is analyzed in a bounded domain with no-flux boundary conditions. The equations are formally derived from a random-walk…
Systems of the type $$\begin{cases} u_t = \nabla \cdot (D_1(u) \nabla u - S_1(u) \nabla v) + f_1(u, v),\\ v_t = \nabla \cdot (D_2(v) \nabla v + S_2(v) \nabla u) + f_2(u, v) \end{cases} \qquad (\star)$$ can be used to model pursuit-evasion…
This work studies the instability of stochastic scalar reaction diffusion equations, driven by a multiplicative noise that is white in time and smooth in space, near to zero, which is assumed to be a fixed point for the equation. We prove…
We discuss applications of a recently developed method for model reduction based on linear response theory of weakly coupled dynamical systems. We apply the weak coupling method to simple stochastic differential equations with slow and fast…
New estimates and global existence results are provided for a class of systems of cross diffusion equations arising from the modeling of chemotaxis with local sensing, possibly featuring a growth term of logistic-type as well. For sublinear…
Given a reaction-advection-diffusion system modelling the sulphation phenomenon, we derive a single regularised non-conservative and path-dependent nonlinear partial differential equation and propose a probabilistic interpretation via a…
The equilibrium distribution function determines macroscopic observables in statistical physics. While conventional methods correct equilibrium distributions in weakly nonlinear or near-integrable systems, they fail in strongly nonlinear…
Stochastic models share many characteristics with generic parametric models. In some ways they can be regarded as a special case. But for stochastic models there is a notion of weak distribution or generalised random variable, and the same…
The macroscopic behavior of dissipative stochastic partial differential equations usually can be described by a finite dimensional system. This article proves that a macroscopic reduced model may be constructed for stochastic…
This paper is a continuation of the work presented in [Chertock et al., Math. Cli. Weather Forecast. 5, 1 (2019), 65--106]. We study uncertainty propagation in warm cloud dynamics of weakly compressible fluids. The mathematical model is…
We apply Malliavin calculus to the $\Phi^4_3$ equation on the torus and prove existence of densities for the solution of the equation evaluated at regular enough test functions. We work in the framework of regularity structures and rely on…
We consider a class of one-dimensional nonlinear stochastic parabolic problems associated with Sellers and Budyko diffusive energy balance climate models with a Legendre weighted diffusion and an additive cylindrical Wiener processes…
Diffusion models have emerged as powerful tools for generative modeling, demonstrating exceptional capability in capturing target data distributions from large datasets. However, fine-tuning these massive models for specific downstream…
Various phenomenological models of particle multiplicity distributions are discussed using a general form of a unified model which is based on the grand canonical partition function and Feynman's path integral approach to statistical…
In this paper we study a recently derived mathematical model for nonlinear propagation of waves in the atmosphere, for which we establish the local well-posedness in the setting of classical solutions. This is achieved by formulating the…