72 citations · 455 across the 28 of their papers we have counts for
6 papers · 1 filter
Global solvability of a model for tuberculosis granuloma formation
Mario Fuest, Johannes Lankeit, Masaaki Mizukami
We discuss a nonlinear system of partial differential equations modelling the formation of granuloma during tuberculosis infections and prove the global solvability of the homogene…
Finite-time blow-up in fully parabolic quasilinear Keller-Segel systems with supercritical exponents
Xinru Cao, Mario Fuest
We examine the possibility of finite-time blow-up of solutions to the fully parabolic quasilinear Keller--Segel model \begin{align}\tag{}\label{prob:star} \begin{cases} u_t…
Location of blow-up points in fully parabolic chemotaxis systems with spatially heterogeneous logistic source
Mario Fuest, Johannes Lankeit, Masaaki Mizukami
We consider the fully parabolic, spatially heterogeneous chemotaxis-growth system \begin{align*} \begin{cases} u_t = Δu - \nabla\cdot(u\nabla v) + κ(x)u-μ(x)u^2, \\ v_t = Δv - v +…
Upper estimates for the Hausdorff dimension of the temporal singular set in chemotaxis-fluid systems
Mario Fuest
The chemotaxis-fluid system \begin{align}\tag{}\label{prob:star} \begin{cases} n_t + u \cdot \nabla n = Δn - \nabla \cdot (n \nabla c), \\ c_t + u \cdot \nabla c = Δc - nc,…
Classical and generalized solutions of an alarm-taxis model
Mario Fuest, Johannes Lankeit
In bounded, spatially two-dimensional domains, the system \begin{equation*} \left\lbrace\begin{alignedat}{3} u_t &= d_1 Δu && &&+ u(λ_1 - μ_1 u - a_1 v - a_2 w), \\ v_t &= d_2 Δv &…
Uniform estimates for solutions to the inhomogeneous 2D Navier-Stokes equations and application to a chemotaxis-fluid system with local sensing
Mario Fuest, Michael Winkler
The chemotaxis-Navier-Stokes system \begin{equation*}\label{1} \left\{ \begin{array}{rcl} n_t+u\cdot\nabla n &=& Δ\big(n c^{-α} \big), \\[1mm] c_t+ u\cdot\nabla c &=& Δc -nc,\\[1mm…