7 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…
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=Îv -μ+u,\q…
Existence, uniqueness, and long-time asymptotic behavior of regular solutions in multidimensional thermoelasticity
Piotr MichaÅ Bies, Tomasz CieÅlak, 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…
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…
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…
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 = Îu - \nabla\cdot(u\nabla v) + κ(x)u-μ(x)u^2, \\ v_t = Îv -…