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We consider a stochastic lattice Cahn-Hilliard equation with nonautonomous nonlinear noise. First, we prove the existence of pullback random attractors in $\ell^2$ for the generated nonautonomous random dynamical system. Then, we construct the time-d
Externí odkaz:
http://arxiv.org/abs/2404.14798
Autor:
Rudnicki, Ryszard
The paper below is a written version of the 17th Andrzej Lasota Lecture presented on January 12th, 2024 in Katowice. During the lecture we tried to show the impact of Andrzej Lasota's results on the author's research concerning various fields of math
Externí odkaz:
http://arxiv.org/abs/2404.09783
Autor:
Carvalho, Silas L., Condori, Alexander
In this work, we are interested in characterizing typical (generic) dimensional properties of invariant measures associated with the full-shift system, $T$, in a product space whose alphabet is a countable set. More specifically, we show that the set
Externí odkaz:
http://arxiv.org/abs/2403.17398
This article provides a case study for a recently introduced diffusion in the space of probability measures over the reals, namely rearranged stochastic heat, which solves a stochastic partial differential equation valued in the set of symmetrised qu
Externí odkaz:
http://arxiv.org/abs/2403.16140
Autor:
Liu, Zhenxin, Shi, Zhiyuan
In this paper, we investigate the stochastic Burgers equation with multiplicative noise defined on the entire real line. The equation can be expressed as follows: $$ \dfrac{\partial u}{\partial t}=\dfrac{\partial^2 u}{\partial x^2}-ku +\dfrac{1}{2}\d
Externí odkaz:
http://arxiv.org/abs/2401.15349
Autor:
Tahraoui, Yassine, Cipriano, Fernanda
This work aims to investigate the well-posedness and the existence of ergodic invariant measures for a class of third grade fluid equations in bounded domain $D\subset\mathbb{R}^d,d=2,3,$ in the presence of a multiplicative noise. First, we show the
Externí odkaz:
http://arxiv.org/abs/2401.04566
We study the vanishing Mach number limit for the stochastic Navier-Stokes equations with $\gamma$-type pressure laws, with focus on the one-dimensional case. We prove that, if the stochastic term vanishes with respect to the Mach number sufficiently
Externí odkaz:
http://arxiv.org/abs/2311.14660
Autor:
Rudnicki Ryszard
Publikováno v:
Annales Mathematicae Silesianae, Vol 38, Iss 2, Pp 134-154 (2024)
The paper below is a written version of the 17th Andrzej Lasota Lecture presented on January 12th, 2024 in Katowice. During the lecture we tried to show the impact of Andrzej Lasota’s results on the author’s research concerning various fields of
Externí odkaz:
https://doaj.org/article/bf1003717a3048ae9568aa32244cc26e
This work introduces a general framework for establishing the long time accuracy for approximations of Markovian dynamical systems on separable Banach spaces. Our results illuminate the role that a certain uniformity in Wasserstein contraction rates
Externí odkaz:
http://arxiv.org/abs/2302.01461
Autor:
Vladimirov, Igor G., Petersen, Ian R.
This paper considers a class of open quantum systems with an algebraic structure of dynamic variables, including the Pauli matrices for finite-level systems as a particular case. The Hamiltonian and the operators of coupling of the system to the exte
Externí odkaz:
http://arxiv.org/abs/2210.06757