Related papers: Evolution Equations in Functional Derivatives of M…
We establish the existence and uniqueness of mild solutions for the polyatomic ellipsoidal BGK model, which is a relaxation type kinetic model describing the evolution of polyatomic gaseous system at the mesoscopic level.
Functional evolution equations are used in the modeling of numerous physical processes. In this work, our main tool is perturbation theory of strongly continuous semigroups. The advantage of this technique is that one can provide functional…
Theoretical methods based on the density matrix are powerful tools to describe open quantum systems. However, such methods are complicated and intricate to be used analytically. Here we present an object-oriented framework for constructing…
We consider evolution differential equations in Fr\'echet spaces that possess unconditional Schauder basis and construct a version of the majorant functions method to obtain existence theorems for Cauchy problems. Applications to PDE and…
A method of solving Maxwell equations in a vicinity of a multipole particle (moving along an arbitrary trajectory) is proposed. The method is based on a geometric construction of a trajectory-adapted coordinate system, which simplifies…
The process of equilibration of a colliding hard-disks system is studied in the framework of classical mechanic. The method consists of dividing the nonequilibrium system into the interacting subsystems; the evolution one of these…
We consider the dynamics of $N$ bosons in three dimensions. We assume the pair interaction is given by $N^{3\beta -1}V(N^{\beta }\cdot )$ . By studying an associated many-body wave operator, we introduce a BBGKY hierarchy which takes into…
The rigorous approach to the description of the kinetic evolution of a many-particle system composed of a trace hard sphere and an environment of finitely many hard spheres is developed. We prove that the evolution of states of a trace hard…
We consider a system of classical particles, interacting via a smooth, long-range potential, in the mean-field regime, and we optimally analyze the propagation of chaos in form of sharp estimates on many-particle correlation functions.…
Given a fine-scale physical theory characterized by an evolutionary system of equations and a set of quantities, defined from the variables of the fine theory, that serve as a coarse representation of the fine scale phenomena, a systematic…
We consider stochastic versions of the Cauchy exponential functional equation and give a martingale characterization of the general solution.
We make several remarks on the B-JIMWLK hierarchy. First, we present a simple and instructive derivation of this equation by considering an arbitrary projectile wave function with small number of valence gluons. We also generalize the…
We study a class of evolutionary partial differential systems with two components related to second order (in time) non-evolutionary equations of odd order in spatial variable. We develop the formal diagonalisation method in symbolic…
In this paper, we define an operator function as a series of operators corresponding to the Taylor series representing the function of the complex variable. In previous papers, we considered the case when a function has a decomposition in…
The expansion of a classical Hamilton formalism consisting in adaptation of it to describe the nonequilibrium systems is offered. Expansion is obtained by construction of formalism on the basis of the dynamics equation of the equilibrium…
Macroscopic equations arising out of stochastic particle systems in detailed balance (called dissipative systems or gradient flows) have a natural variational structure, which can be derived from the large-deviation rate functional for the…
We construct birth-and-death Markov evolution of states(distributions) of point particle systems in $\mathbb{R}^d$. In this evolution, particles reproduce themselves at distant points (disperse) and die under the influence of each other…
In this paper, we study the Cauchy problems for weakly coupled systems of semi-linear structurally damped $\sigma$-evolution models with different power nonlinearities. By assuming additional $L^m$ regularity on the initial data, with $m…
Boolean Delay Equations (BDEs) are semi-discrete dynamical models with Boolean-valued variables that evolve in continuous time. Systems of BDEs can be classified into conservative or dissipative, in a manner that parallels the…
The study of biological cells in terms of mesoscopic, nonequilibrium, nonlinear, stochastic dynamics of open chemical systems provides a paradigm for other complex, self-organizing systems with ultra-fast stochastic fluctuations, short-time…