We recount and discuss some of the most important methods and blow-up criteria for
analyzing solutions of Keller-Segel chemotaxis models. First, we discuss the results …

This work deals with a parabolic chemotaxis model with nonlinear diffusion and nonlocal
reaction source. The problem is formulated on the whole space and, depending on a …

This book presents models written as partial differential equations and originating from
various questions in population biology, such as physiologically structured equations …

As a counterpoint to classical stochastic particle methods for diffusion, we develop a
deterministic particle method for linear and nonlinear diffusion. At first glance, deterministic …

Γ vt= v− λv+ u in Ω×(0, T), in a domain Ω of RN with N⩾ 1, where m, Γ> 0, λ⩾ 0 are constants
and T> 0. When Ω= RN, we impose the Neumann boundary conditions on the boundary …

We prove the global existence, along with some basic boundedness properties, of weak
solutions to a PDE-ODE system modeling the multiscale invasion of tumor cells through the …

In this paper, we are concerned with a model arising from biology, which is a coupled
system of the chemotaxis equations and the viscous incompressible fluid equations through …

We consider a model arising from biology, consisting of chemotaxis equations coupled to
viscous incompressible fluid equations through transport and external forcing. Global …

We consider a model system for the collective behavior of oxygen-driven swimming bacteria
in an aquatic fluid. In certain parameter regimes, such suspensions of bacteria feature large …

We prove the mean field limit and quantitative estimates for many-particle systems with
singular attractive interactions between particles. As an important example, a full rigorous …