arXiv subjects

Adrian Tudorascu

Publications and source records attributed to Adrian Tudorascu.

4 recordsLinked to original sources

arXiv2026

On the asymptotic behavior of the Repulsive Pressureless Euler-Poisson System

The main objective of this paper is a study of the asymptotic behavior of distributional solutions to the one-dimensional repulsive pressureless Euler-Poisson system. The system is a model for the dynamics of a mass distribution evolving on \mathbb{R} whose masses exert outward forces on one another. A discrete (describing the evolution of finitely many particles) solution is called sticky if, upon collision, particles stick together and move as one for all subsequent time, according to the conservation of mass and momentum principles. We prove results on the total energy (Hamiltonian) of the system and demonstrate the existence and uniqueness of so-called "perfect" states, where the Hamiltonian is constant over all time and the solution converges to equilibrium, a single stationary particle. We provide a necessary and a sufficient condition for finite-time collapse, and present a quadratic envelope within which a solution must remain in order to collapse. We demonstrate various (counter)examples that illustrate the unique behavior of the repulsive scheme with the sticky condition, analytically and with a computer simulation.

math.AP↗

arXiv2023

Asymptotics of the Sticky Particles evolution

We study the long-time asymptotic behavior of the Sticky Particles dynamics on the real line. The time average of the Sticky Particles Lagrangian map has a limit which arises as a general property of projections onto closed convex cones in Hilbert spaces. More notably, we prove that the map itself has an asymptotic limit in the case where the Sticky Particles dynamics is confined to a compact set.

math.AP↗

arXiv2018

Convergence to the complex balanced equilibrium for some chemical reaction-diffusion systems with boundary equilibria

In this paper we study the rate of convergence to the complex balanced equilibrium for some chemical reaction-diffusion systems with boundary equilibria. We first analyze a three-species system with boundary equilibria in some stoichiometric classes, and whose right hand side is bounded above by a quadratic nonlinearity in the positive orthant. We prove similar results on the convergence to the positive equilibrium for a fairly general two-species reversible reaction-diffusion network with boundary equilibria.

math.AP↗

arXiv2017

Chemical reaction-diffusion networks; convergence of the method of lines

We show that solutions of the chemical reaction-diffusion system associated to $A+B\rightleftharpoons C$ in one spatial dimension can be approximated in $L^2$ on any finite time interval by solutions of a space discretized ODE system which models the corresponding chemical reaction system replicated in the discretization subdomains where the concentrations are assumed spatially constant. Same-species reactions through the virtual boundaries of adjacent subdomains lead to diffusion in the vanishing limit. We show convergence of our numerical scheme by way of a consistency estimate, with features generalizable to reaction networks other than the one considered here, and to multiple space dimensions. In particular, the connection with the class of complex-balanced systems is briefly discussed here, and will be considered in future work.

math.NA↗