18 citations · 36 across the 12 of their papers we have counts for
14 papers
Existence and stability of non-equilibrium steady states of a weakly non-linear kinetic Fokker-Planck equation in a domain
J Evans, R Medina
We study a weakly non-linear Fokker-Planck equation with BGK heat thermostats in a spatially bounded domain with conservative Maxwell boundary conditions, presenting a space-depend…
Sub-exponential tails in biased run and tumble equations with unbounded velocities
Émeric Bouin, Josephine Evans, Luca Ziviani
Run and tumble equations are widely used models for bacterial chemotaxis. In this paper, we are interested in the long time behaviour of run and tumble equations with unbounded vel…
Trend to equilibrium for run and tumble equations with non-uniform tumbling kernels
Josephine Evans, Havva Yoldaş
We study the long-time behaviour of a run and tumble model which is a kinetic-transport equation describing bacterial movement under the effect of a chemical stimulus. The experime…
Properties of Non-Equilibrium Steady States for the non-linear BGK equation on the torus
Josephine Evans, Angeliki Menegaki
We study the non-linear BGK model in 1d coupled to a spatially varying thermostat. We show existence, local uniqueness and linear stability of a steady state when the linear coupli…
Steady states of an Elo-type rating model for players of varying strength
Bertram Düring, Josephine Evans, Marie-Therese Wolfram
In this paper we study the long-time behaviour of a kinetic formulation of an Elo-type rating model for a large number of interacting players with variable strength. The model resu…
Finding the jump rate for fastest decay in the Goldstein-Taylor model
Helge Dietert, Josephine Evans
For hypocoercive linear kinetic equations we first formulate an optimisation problem on a spatially dependent jump rate in order to find the fastest decay rate of perturbations. In…
On the asymptotic behaviour of a run and tumble equation for bacterial chemotaxis
Josephine Evans, Havva Yoldaş
We prove that linear and weakly non-linear run and tumble equations converge to a unique steady state solution with an exponential rate in a weighted total variation distance. In t…
Existence of a Non-Equilibrium Steady State for the Non-linear BGK equation on an interval
Josephine Evans, Angeliki Menegaki
We show existence of a non-equilibrium steady state for the one-dimensional, non-linear BGK model on an interval with diffusive boundary conditions. These boundary conditions repre…
Quantitative Rates of Convergence to Equilibrium for the Degenerate Linear Boltzmann equation on the Torus
Josephine Evans, Ivan Moyano
We study the linear relaxation Boltzmann equation on the torus with a spatially varying jump rate which can be zero on large sections of the domain. In \cite{BS13} Bernard and Salv…
Hypocoercivity of linear kinetic equations via Harris's Theorem
José A. Cañizo, Chuqi Cao, Josephine Evans +1
We study convergence to equilibrium of the linear relaxation Boltzmann (also known as linear BGK) and the linear Boltzmann equations either on the torus $(x,v) \in \mathbb{T}^d \ti…
Hypocoercivity in Wasserstein-1 for the kinetic Fokker-Planck equation via Malliavin Calculus
Josephine Evans
We study the kinetic Fokker-Planck equation on the whole space with a confining potential. We show quantitative rates of exponential convergence to equilibrium in a well chosen Was…
Hypocoercivity in Phi-entropy for the Linear Relaxation Boltzmann Equation on the Torus
Josephine Evans
This paper studies convergence to equilibrium for the spatially inhomogeneous linear relaxation Boltzmann equation in Boltzmann entropy and related entropy functionals the -entr…
Non-Equilibrium Steady States in Kac's Model Coupled to a Thermostat
Josephine Evans
This paper studies the existence, uniqueness and convergence to non-equilibrium steady states in Kac's model with an external coupling. We work in both Fourier distances and Wasser…
Convergence to equilibrium for the kinetic Fokker-Planck equation on the torus
Helge Dietert, Josephine Evans, Thomas Holding
We study convergence to equilibrium for the kinetic Fokker-Planck equation on the torus. Solving the stochastic differential equation, we show exponential convergence in the Monge-…