72 citations · 455 across the 28 of their papers we have counts for
29 papers
Absence of critical mass phenomena in one-dimensional critical quasilinear Keller-Segel systems
Xinru Cao, Mario Fuest
We consider the Neumann initial boundary value problem associated to the chemotaxis system \begin{align}\label{prob:abstract}\tag{} \begin{cases} u_t = \big((u+1)^{m-1} u_x…
Existence, uniqueness, and long-time asymptotic behavior of regular solutions in multidimensional thermoelasticity
Piotr Michał Bies, Tomasz Cieślak, Mario Fuest +3
We study a simplified nonlinear thermoelasticity model on two- and three-dimensional tori. A novel functional involving the Fisher information associated with temperature is introd…
Shrinking vs. expanding: the evolution of spatial support in degenerate Keller-Segel systems
Mario Fuest, Frederic Heihoff
We consider radially symmetric solutions of the degenerate Keller-Segel system \begin{align*} \begin{cases} \partial_t u=\nabla\cdot (u^{m-1}\nabla u - u\nabla v),\\ 0=Δv -μ+u,\qua…
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…
A cross-diffusion system modelling rivaling gangs: global existence of bounded solutions and FCT stabilization for numerical simulation
Mario Fuest, Shahin Heydari
For the gang territoriality model \begin{align*} \begin{cases} u_t = D_u Δu + χ_u \nabla \cdot (u \nabla w), \\ v_t = D_v Δv + χ_v \nabla \cdot (v \nabla z), \\ w_t = -w + \frac{v}…
Corners and collapse: Some simple observations concerning critical masses and boundary blow-up in the fully parabolic Keller-Segel system
Mario Fuest, Johannes Lankeit
Our main result shows that the mass is critical for the minimal Keller-Segel system \begin{align}\label{prob:abstract}\tag{} \begin{cases} u_t = Δu - \nabla \cdot (u \n…
On the existence of global solutions for the 3D chemorepulsion system
Tomasz Cieślak, Mario Fuest, Karol Hajduk +1
In this paper, we give sufficient conditions for global-in-time existence of classical solutions for the fully parabolic chemorepulsion system posed on a convex, bounded three-dime…
Critical mass phenomena in higher dimensional quasilinear Keller-Segel systems with indirect signal production
Mario Fuest, Johannes Lankeit, Yuya Tanaka
In this paper, we deal with quasilinear Keller--Segel systems with indirect signal production, $$\begin{cases} u_t = \nabla \cdot ((u+1)^{m-1}\nabla u) - \nabla \cdot (u \nabla v),…
Chemotaxis(-fluid) systems with logarithmic sensitivity and slow consumption: global generalized solutions and eventual smoothness
Mario Fuest
We consider the system \begin{align*} \begin{cases} n_t + u \cdot \nabla n = Δn - χ\nabla \cdot (\frac{n}{c} \nabla c), \\ c_t + u \cdot \nabla c = Δc - nf(c), \\ u_t + (u \cdot \n…
Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source
Tobias Black, Mario Fuest, Johannes Lankeit +1
We discuss the influence of possible spatial inhomogeneities in the coefficients of logistic source terms in parabolic-elliptic chemotaxis-growth systems of the form \begin{align*}…
Global existence of classical solutions and numerical simulations of a cancer invasion model
Mario Fuest, Shahin Heydari, Petr Knobloch +2
In this paper, we study a cancer invasion model both theoretically and numerically. The model is a nonstationary, nonlinear system of three coupled partial differential equations m…
Strong convergence of weighted gradients in parabolic equations and applications to global generalized solvability of cross-diffusive systems
Mario Fuest
In the first part of the present paper, we show that strong convergence of in and weak convergence of $(f_{\varepsilon})_{\v…
Unboundedness phenomenon in a model of urban crime
Mario Fuest, Frederic Heihoff
We show that spatial patterns ("hotspots") may form in the crime model \begin{equation} \left\{\; \begin{aligned} u_{t} &= \tfrac{1}{\varepsilon}Δu - \tfracχ{\varepsilon} \nabla \c…
Global weak solutions to fully cross-diffusive systems with nonlinear diffusion and saturated taxis sensitivity
Mario Fuest
Systems of the type $$\begin{cases} u_t = \nabla \cdot (D_1(u) \nabla u - S_1(u) \nabla v) + f_1(u, v),\\ v_t = \nabla \cdot (D_2(v) \nabla v + S_2(v) \nabla u) + f_2(u, v) \end{ca…
On the optimality of upper estimates near blow-up in quasilinear Keller--Segel systems
Mario Fuest
Solutions to the chemotaxis system \begin{align*} \begin{cases} u_t = \nabla \cdot ( (u+1)^{m-1} \nabla u - u (u+1)^{q-1} \nabla v), \\ τv_t = Δv - v + u \end{cases} \end{…
Approaching optimality in blow-up results for Keller-Segel systems with logistic-type dampening
Mario Fuest
Nonnegative solutions of the Neumann initial-boundary value problem for the chemotaxis system \begin{align}\label{prob:star}\tag{} \begin{cases} u_t = Δu - \nabla \cdot (u \…
Relaxed parameter conditions for chemotactic collapse in logistic-type parabolic-elliptic Keller-Segel systems
Tobias Black, Mario Fuest, Johannes Lankeit
We study the finite-time blow-up in two variants of the parabolic-elliptic Keller-Segel system with nonlinear diffusion and logistic source. In -dimensional balls, we consider \…
Long-term behaviour in a parabolic-elliptic chemotaxis-consumption model
Mario Fuest, Johannes Lankeit, Masaaki Mizukami
Global existence and boundedness of classical solutions of the chemotaxis--consumption system \begin{align*} n_t &= Δn - \nabla \cdot (n \nabla c), \\ 0 &= Δc - nc, \end{align*} un…
When do Keller-Segel systems with heterogeneous logistic sources admit generalized solutions?
Jianlu Yan, Mario Fuest
We construct global generalized solutions to the chemotaxis system \begin{align*} \begin{cases} u_t = Δu - \nabla \cdot (u \nabla v) + λ(x) u - μ(x) u^κ,\\ v_t = Δv - v + u \end{ca…