From the 1 of 300 papers with an AI index.
29.3k citations
- Beijing Institute of TechnologyCN11 papers
- Max Planck Institute for the Science of LightDE11 papers
- Leipzig UniversityDE9 papers
- TU Dortmund UniversityDE8 papers
- Institute of PhysicsPL7 papers
- Ruhr University BochumDE6 papers
- Technical University of MunichDE6 papers
- Centre National de la Recherche ScientifiqueFR5 papers
- Ioffe InstituteRU5 papers
- University of ArizonaUS5 papers
- Australian National UniversityAU4 papers
- ETH ZurichCH4 papers
15 papers · 1 filter
A critical blow-up exponent for flux limitation in a Keller-Segel system
Michael Winkler
The parabolic-elliptic cross-diffusion system \[ \left\{ \begin{array}{l} u_t = Δu - \nabla \cdot \Big(uf(|\nabla v|^2) \nabla v \Big), \\[1mm] 0 = Δv - μ+ u, \qquad \int_Ωv=0, \qq…
Conditional estimates in three-dimensional chemotaxis-Stokes systems and application to a Keller-Segel-fluid model accounting for gradient-dependent flux limitation
Michael Winkler
This manuscript deals with the three-dimensional version of a flux-limited Keller-Segel system coupled to the incompressible Stokes equations through transport and buoyancy. The ma…
Immediate smoothing and global solutions for initial data in in a Keller-Segel system with logistic terms in 2D
Johannes Lankeit
This article deals with the logistic Keller-Segel model \[ \begin{cases} u_t = Δu - χ\nabla\cdot(u\nabla v) + κu - μu^2, \\ \\ v_t = Δv - v + u \end{cases} \] in bounded two-dimens…
Stationary solutions to a chemotaxis-consumption model with realistic boundary conditions
Marcel Braukhoff, Johannes Lankeit
Previous studies of chemotaxis models with consumption of the chemoattractant (with or without fluid) have not been successful in explaining pattern formation even in the simplest…
Continuation beyond interior gradient blow-up in a semilinear parabolic equation
Marek Fila, Johannes Lankeit
It is known that there is a class of semilinear parabolic equations for which interior gradient blow-up (in finite time) occurs for some solutions. We construct a continuation of s…
Analysis of a one-dimensional forager-exploiter model
Youshan Tao, Michael Winkler
\begin{abstract} \noindent % We consider the one-dimensional parabolic system The system \bas \left\{ \begin{array}{l} u_t= u_{xx} - χ_1 (uw_x)_x, \\[1mm] v_t = v_{xx} - χ_2 (vu_x)…