Related papers: The microscopic derivation and well-posedness of t…
The Keller-Segel equation, a classical chemotaxis model, and many of its variants have been extensively studied for decades. In this work, we focus on 3D Keller-Segel equation with a quadratic logistic damping term $-\mu \rho^2$ (modeling…
We consider stochastic reaction-diffusion equations on a finite network represented by a finite graph. On each edge in the graph a multiplicative cylindrical Gaussian noise driven reaction-diffusion equation is given supplemented by a…
We prove that an averaging principle holds for a general class of stochastic reaction-diffusion systems, having unbounded multiplicative noise, in any space dimension. We show that the classical Khasminskii approach for systems with a…
A simple proof of the existence of solutions for the two-dimensional Keller-Segel model with measures with all the atoms less than $8\pi$ as the initial data is given. This result has been obtained by Senba--Suzuki and Bedrossian--Masmoudi…
In this paper, we study the relationship between a diffusive model and a non-diffusive model which are both derived from the well-known Keller-Segel model, as a coefficient of diffusion $\varepsilon$ goes to zero. First, we establish the…
It is of great biological interest to understand the molecular origins of chemotactic behavior of E. coli by developing population-level models based on the underlying signaling pathway dynamics. We derive macroscopic models for E.coli…
The technique of stochastic solutions, previously used for deterministic equations, is here proposed as a solution method for partial differential equations driven by distribution-valued noises.
We investigate the numerical discretization of a two-stream kinetic system with an internal state, such system has been introduced to model the motion of cells by chemotaxis. This internal state models the intracellular methylation level.…
A semi-classical non-Hamiltonian model of a spontaneous collapse of unstable quantum system is given. The time evolution of the system becomes non-Hamiltonian at random instants of transition of pure states to reduced ones, given by a…
In this paper, we are interested in the analytical study of a nonlinear Stochastic Partial Differential Equation (SPDE) arising as a model of phytoplankton aggregation. This SPDE consists in a diffusion equation with a chemotaxis term…
We consider a parabolic-elliptic Keller-Segel system with spatially dependent diffusion sensitivity \begin{eqnarray*} \left\{ \begin{array}{l} u_t = \nabla \cdot (|x|^\beta \nabla u) - \nabla \cdot (u\nabla v), \\[1mm] 0 = \Delta v - \mu +…
This work presents an alternative approach to obtain the quantum field equations in curved spacetime, considering that sufficiently small particles follow stochastic trajectories around geodesic. Our proposal is based on a stochastic…
In this paper we investigate pattern formation in Keller--Segel chemotaxis models over a multi--dimensional bounded domain subject to homogeneous Neumann boundary conditions. It is shown that the positive homogeneous steady state loses its…
Population cross-diffusion systems of Shigesada-Kawasaki-Teramoto type are derived in a mean-field-type limit from stochastic, moderately interacting many-particle systems for multiple population species in the whole space. The diffusion…
We study the Cauchy problem for the chemotaxis Navier-Stokes equations and the Keller-Segel-Navier-Stokes system. Local-in-time and global-in-time solutions satisfying fundamental properties such as mass conservation and nonnegativity…
We present a Bayesian non-parametric way of inferring stochastic differential equations for both regression tasks and continuous-time dynamical modelling. The work has high emphasis on the stochastic part of the differential equation, also…
This paper deals with the homogeneous Neumann boundary-value problem for the Keller--Segel system \begin{align*} \begin{cases} u_t=\Delta u - \chi \nabla \cdot (u|\nabla v|^{p-2}\nabla v),\\[] v_t=\Delta v - v + u^{\theta} \end{cases}…
We formulate a short-time expansion for one-dimensional Fokker-Planck equations with spatially dependent diffusion coefficients, derived from stochastic processes with Gaussian white noise, for general values of the discretization parameter…
In recent works it has been demonstrated that using an appropriate rescaling, linear Boltzmann-type equations give rise to a scalar fractional diffusion equation in the limit of a small mean free path. The equilibrium distributions are…
We consider a particle system with a mean-field-type interaction perturbed by some common and individual noises. When the interacting kernels are sublinear and only locally Lipschitz-continuous, relying on arguments based on the tightness…