72 citations · 455 across the 28 of their papers we have counts for
6 papers · 1 filter
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…
Global solutions near homogeneous steady states in a multi-dimensional population model with both predator- and prey-taxis
Mario Fuest
We study the system \begin{align*}\label{prob:star} \tag{} \begin{cases} u_t = D_1 Δu - χ_1 \nabla \cdot (u \nabla v) + u(λ_1 - μ_1 u + a_1 v) \\ v_t = D_2 Δv + χ_2 \nabla \…