341 citations · 701 across the 10 of their papers we have counts for
11 papers
Rate of convergence to equilibrium for the heated string
Tomasz Cieślak, Jacek Jendrej, Christian Stinner
In the present manuscript, we calculate the exponential rate of convergence of the heated string system (a mixed-type hyperbolic-parabolic system of PDEs) towards the equilibrium,…
Singular limit of a chemotaxis model with indirect signal production and phenotype switching
Philippe Laurençot, Christian Stinner
Convergence of solutions to a partially diffusive chemotaxis system with indirect signal production and phenotype switching is shown in a two-dimensional setting when the switching…
Mass threshold for infinite-time blowup in a chemotaxis model with splitted population
Philippe Laurençot, Christian Stinner
We study the chemotaxis model t u = div(u -- uw) + v -- u in (0, ) x , t v = u -- v in (0, ) x , t w =…
Modeling multiple taxis: tumor invasion with phenotypic heterogeneity, haptotaxis, and unilateral interspecies repellence
Niklas Kolbe, Nikolaos Sfakianakis, Christian Stinner +2
We provide a short review of existing models with multiple taxis performed by (at least) one species and consider a new mathematical model for tumor invasion featuring two mutually…
Instantaneous shrinking and single point extinction for viscous Hamilton-Jacobi equations with fast diffusion
Razvan Gabriel Iagar, Philippe Laurençot, Christian Stinner
For a large class of non-negative initial data, the solutions to the quasilinear viscous Hamilton-Jacobi equation in …
New critical exponents in a fully parabolic quasilinear Keller-Segel and applications to volume filling models
Tomasz Cieślak, Christian Stinner
We carry on our studies related to the fully parabolic quasilinear Keller-Segel system started in [6] and continued in [7]. In the above mentioned papers we proved finite-time blow…
Finite-time blowup in a supercritical quasilinear parabolic-parabolic Keller-Segel system in dimension 2
Tomasz Cieślak, Christian Stinner
In this paper we prove finite-time blowup of radially symmetric solutions to the quasilinear parabolic-parabolic two-dimensional Keller-Segel system for any positive mass. This is…
Finite-time blowup and global-in-time unbounded solutions to a parabolic-parabolic quasilinear Keller-Segel system in higher dimensions
Tomasz Cieślak, Christian Stinner
In this paper we consider quasilinear Keller-Segel type systems of two kinds in higher dimensions. In the case of a nonlinear diffusion system we prove an optimal (with respect to…
Convergence to separate variables solutions for a degenerate parabolic equation with gradient source
Philippe Laurencot, Christian Stinner
The large time behaviour of nonnegative solutions to a quasilinear degenerate diffusion equation with a source term depending solely on the gradient is investigated. After a suitab…
Refined asymptotics for the infinite heat equation with homogeneous Dirichlet boundary conditions
Philippe Laurencot, Christian Stinner
The nonnegative viscosity solutions to the infinite heat equation with homogeneous Dirichlet boundary conditions are shown to converge as time increases to infinity to a uniquely d…
Convergence to steady states for radially symmetric solutions to a quasilinear degenerate diffusive Hamilton-Jacobi equation
Guy Barles, Philippe Laurençot, Christian Stinner
Convergence to a single steady state is shown for non-negative and radially symmetric solutions to a diffusive Hamilton-Jacobi equation with homogeneous Dirichlet boundary conditio…