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Approaching optimality in blow-up results for Keller-Segel systems with logistic-type dampening

- Mario Fuest
- Mathematics, Physics
- 2 July 2020

Nonnegative solutions of the Neumann initial-boundary value problem for the chemotaxis system \begin{align}\label{prob:star}\tag{$\star$} \begin{cases} u_t = \Delta u - \nabla \cdot (u \nabla v) +… Expand

Relaxed parameter conditions for chemotactic collapse in logistic-type parabolic-elliptic Keller-Segel systems

- T. Black, Mario Fuest, Johannes Lankeit
- Mathematics, Physics
- 25 May 2020

We study the finite-time blow-up in two variants of the parabolic--elliptic Keller--Segel system with nonlinear diffusion and logistic source. In $n$-dimensional balls, we consider \begin{align*} … Expand

On the optimality of upper estimates near blow-up in quasilinear Keller--Segel systems

- Mario Fuest
- Mathematics, Physics
- 27 July 2020

Solutions $(u, v)$ 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), \\
\tau v_t = \Delta v - v + u
\end{cases}… Expand

Finite-time blow-up in a two-dimensional Keller–Segel system with an environmental dependent logistic source

- Mario Fuest
- Physics, Mathematics
- 11 May 2019

Abstract The Neumann initial–boundary problem for the chemotaxis system ( ⋆ ) u t = Δ u − ∇ ⋅ ( u ∇ v ) + κ ( | x | ) u − μ ( | x | ) u p , 0 = Δ v − m ( t ) | Ω | + u , m ( t ) ≔ ∫ Ω u ( ⋅ , t ) is… Expand

Analysis of a chemotaxis model with indirect signal absorption

- Mario Fuest
- Mathematics
- 21 January 2019

Abstract We consider the chemotaxis model { u t = Δ u − ∇ ⋅ ( u ∇ v ) , v t = Δ v − v w , w t = − δ w + u in smooth, bounded domains Ω ⊂ R n , n ∈ N , where δ > 0 is a given parameter. If either n ≤… Expand

Boundedness enforced by mildly saturated conversion in a chemotaxis-May–Nowak model for virus infection

- Mario Fuest
- Mathematics
- 28 September 2018

Abstract We study the system ( ⋆ ) { u t = Δ u − ∇ ⋅ ( u ∇ v ) − u − f ( u ) w + κ , v t = Δ v − v + f ( u ) w , w t = Δ w − w + v , which models the virus dynamics in an early stage of an HIV… Expand

Long-term behaviour in a parabolic-elliptic chemotaxis-consumption model

- Mario Fuest, Johannes Lankeit, M. Mizukami
- Mathematics, Physics
- 20 April 2020

Global existence and boundedness of classical solutions of the chemotaxis--consumption system \begin{align*}
n_t &= \Delta n - \nabla \cdot (n \nabla c), \\
0 &= \Delta c - nc, \end{align*} under… Expand

Global weak solutions to fully cross-diffusive systems with nonlinear diffusion and saturated taxis sensitivity

- Mario Fuest
- Mathematics
- 26 May 2021

Systems of the type { ut = ∇ · (D1(u)∇u − S1(u)∇v) + f1(u, v), vt = ∇ · (D2(v)∇v + S2(v)∇u) + f2(u, v) (⋆) can be used to model pursuit–evasion relationships between predators and prey. Apart from… Expand

Global Solutions near Homogeneous Steady States in a Multidimensional Population Model with Both Predator- and Prey-Taxis

- Mario Fuest
- Computer Science, Physics
- SIAM J. Math. Anal.
- 9 April 2020

TLDR

Blow-up profiles in quasilinear fully parabolic Keller--Segel systems

- Mario Fuest
- Mathematics, Physics
- 26 September 2019

We examine finite-time blow-up solutions $(u, v)$ to \begin{align} \label{prob:star} \tag{$\star$}
\begin{cases} u_t = \nabla \cdot (D(u, v) \nabla u - S(u, v) \nabla v), v_t = \Delta v - v + u … Expand

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