A generalized solution concept for the Keller-Segel system with logarithmic sensitivity: global solvability for large nonradial data
From MaRDI portal
Publication:2411118
DOI10.1007/s00030-017-0472-8zbMath1373.35166arXiv1701.07391OpenAlexW2581314377MaRDI QIDQ2411118
Michael Winkler, Johannes Lankeit
Publication date: 20 October 2017
Published in: NoDEA. Nonlinear Differential Equations and Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1701.07391
Nonlinear parabolic equations (35K55) Cell movement (chemotaxis, etc.) (92C17) Generalized solutions to partial differential equations (35D99)
Related Items
Global solvability in a two-species chemotaxis system with signal production, Attractiveness of constant states in logistic-type Keller-Segel systems involving subquadratic growth restrictions, Global existence of solutions without Dirac-type singularity to a chemotaxis-fluid system with arbitrary superlinear degradation, A double critical mass phenomenon in a no-flux-Dirichlet Keller-Segel system, Global existence and boundedness of solutions to a chemotaxis system with singular sensitivity and logistic-type source, Global boundedness to a parabolic-parabolic chemotaxis model with nonlinear diffusion and singular sensitivity, Global and exponential attractor of the repulsive Keller–Segel model with logarithmic sensitivity, On the global existence and qualitative behaviour of one-dimensional solutions to a model for urban crime, Boundedness and exponential stabilization in a parabolic-elliptic Keller-Segel model with signal-dependent motilities for local sensing chemotaxis, Generalised supersolutions with mass control for the Keller-Segel system with logarithmic sensitivity, A new result for global solvability in a singular chemotaxis-growth system with indirect signal production, Singular sensitivity in a Keller-Segel-fluid system, Global boundedness of solutions to a parabolic–parabolic chemotaxis system with local sensing in higher dimensions, Global generalized solutions to a parabolic-elliptic Keller-Segel system with singular sensitivity, Stabilization in the logarithmic Keller-Segel system, Generalized solutions for a system of partial differential equations arising from urban crime modeling with a logistic source term, Global existence and boundedness of solutions to a chemotaxis-consumption model with singular sensitivity, Global bounded solutions to a Keller-Segel system with singular sensitivity, Boundedness to a parabolic-parabolic singular chemotaxis system with logistic source, Global existence of weak solutions for the 2D incompressible Keller-Segel-Navier-Stokes equations with partial diffusion, Global generalized solvability in a strongly degenerate taxis-type parabolic system modeling migration-consumption interaction, Eventual smoothness and asymptotic stabilization in a two-dimensional logarithmic chemotaxis-Navier-Stokes system with nutrient-supported proliferation and signal consumption, Global existence in a two-species chemotaxis system with signal-dependent sensitivity and logistic source, Large time behavior of solutions to a chemotaxis system with singular sensitivity and logistic source, $L^1$ solutions to parabolic Keller-Segel systems involving arbitrary superlinear degradation, Boundedness in a logistic chemotaxis system with weakly singular sensitivity in dimension two, On a crime model in higher-dimensional setting: global generalized solvability and eventual smoothness, Global solutions in a chemotaxis consumption model with singular sensitivity, Global existence of classical solutions to a regularized brine inclusion model, Global boundedness in a two-dimensional chemotaxis system with nonlinear diffusion and singular sensitivity, Strong convergence of weighted gradients in parabolic equations and applications to global generalized solvability of cross-diffusive systems, Generalized solution and eventual smoothness in a logarithmic Keller–Segel system for criminal activities, Can Dirac-type singularities in Keller-Segel systems be ruled out by power-type singular sensitivities?, Small-Mass Solutions in the Two-Dimensional Keller--Segel System Coupled to the Navier--Stokes Equations, Global solutions in a fully parabolic chemotaxis system with singular sensitivity and nonlinear signal production, Boundedness in a higher-dimensional singular chemotaxis-growth system with indirect signal production, Global solvability in a two-dimensional singular chemotaxis-fluid system with indirect signal production or consumption, Boundedness and asymptotic behavior of solutions to one-dimensional urban crime system with nonlinear diffusion, Effects of density-suppressed motility in a two-dimensional chemotaxis model arising from tumor invasion, Analysis of long‐time solution of chemotactic model with indirect signal consumption in three‐dimensional case, A chemotaxis system with singular sensitivity for burglaries in the higher-dimensional settings: generalized solvability and long-time behavior, On the existence of generalized solutions to a spatio-temporal predator-prey system with prey-taxis, A quantitative strong parabolic maximum principle and application to a taxis-type migration-consumption model involving signal-dependent degenerate diffusion, On the fractional view analysis of Keller-Segel equations with sensitivity functions, Global generalized solutions to a forager–exploiter model with superlinear degradation and their eventual regularity properties, Global radial renormalized solution to a producer–scrounger model with singular sensitivities, Boundedness of classical solutions for a chemotaxis system with general sensitivity function, Global well-posedness and stability of constant equilibria in parabolic–elliptic chemotaxis systems without gradient sensing, The fast signal diffusion limit in a Keller-Segel system, Classical solutions to a logistic chemotaxis model with singular sensitivity and signal absorption, Stabilization in the Keller–Segel system with signal-dependent sensitivity, On the global generalized solvability of a chemotaxis model with signal absorption and logistic growth terms, A sufficient condition of sensitivity functions for boundedness of solutions to a parabolic-parabolic chemotaxis system, Existence of weak solutions to the Keller-Segel chemotaxis system with additional cross-diffusion, Global existence and asymptotic dynamics in a 3D fractional chemotaxis system with singular sensitivity, Global existence and asymptotic behavior in a two-species chemotaxis system with logistic source, Asymptotic profile of a two-dimensional Chemotaxis–Navier–Stokes system with singular sensitivity and logistic source, Unnamed Item, Global well-posedness of logarithmic Keller-Segel type systems, On a fully parabolic singular chemotaxis-(growth) system with indirect signal production or consumption, Keller-Segel chemotaxis models: a review, Global existence of solutions to a fully parabolic chemotaxis system with singular sensitivity and logistic source, Eventual smoothness and stabilization of global weak solutions in parabolic-elliptic chemotaxis systems with logarithmic sensitivity, Global boundedness of classical solutions to a logistic chemotaxis system with singular sensitivity, Global generalized solutions to a Keller-Segel system with nonlinear diffusion and singular sensitivity, Global solvability in a three-dimensional Keller-Segel-Stokes system involving arbitrary superlinear logistic degradation, The logistic chemotaxis system with singular sensitivity and signal absorption in dimension two, A logarithmic chemotaxis model featuring global existence and aggregation, Boundedness and asymptotic behavior to a chemotaxis-fluid system with singular sensitivity and logistic source, Boundedness of classical solutions to a degenerate Keller-Segel type model with signal-dependent motilities, Facing low regularity in chemotaxis systems, Unlimited growth in logarithmic Keller-Segel systems, The role of superlinear damping in the construction of solutions to drift-diffusion problems with initial data in \(L^{1}\), Global existence in a chemotaxis system with singular sensitivity and signal production, Large-time behavior in a two-dimensional logarithmic chemotaxis-Navier-Stokes system with signal absorption, Analysis of a chemotaxis model with indirect signal absorption, Generalized Global Supersolutions with Mass Control for Systems with Taxis, Global existence, boundedness and asymptotic behavior to a chemotaxis model with singular sensitivity and logistic source, Global solvability in a two-species chemotaxis system with logistic source, Comparison of two finite element schemes for a chemo-repulsion system with quadratic production, Global existence to a chemotaxis-consumption model with nonlinear diffusion and singular sensitivity, Global solvability and stabilization in a two-dimensional cross-diffusion system modeling urban crime propagation, Global solvability in a Keller-Segel-growth system with indirect signal production, Global generalized solutions to a three species predator-prey model with prey-taxis, Local energy estimates and global solvability in a three-dimensional chemotaxis-fluid system with prescribed signal on the boundary, Boundedness in a chemotaxis-consumption system with singular sensitivity, Global generalized solvability in the Keller-Segel system with singular sensitivity and arbitrary superlinear degradation, Chemotaxis systems with singular sensitivity and logistic source: boundedness, persistence, absorbing set, and entire solutions, A two-dimensional Keller-Segel-Navier-Stokes system with logarithmic sensitivity: generalized solutions and classical solutions, Boundedness in a fully parabolic attraction-repulsion chemotaxis system with nonlinear diffusion and signal-dependent sensitivity, Global existence in reaction-diffusion systems with mass control under relaxed assumptions merely referring to cross-absorptive effects
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Global boundedness of solutions in a parabolic-parabolic chemotaxis system with singular sensitivity
- Boundedness in a fully parabolic chemotaxis system with singular sensitivity
- Persistence of mass in a chemotaxis system with logistic source
- Global weak solutions in a chemotaxis system with large singular sensitivity
- Global existence and boundedness in a parabolic-elliptic Keller-Segel system with general sensitivity
- On the Cauchy problem for Boltzmann equations: Global existence and weak stability
- Aggregation vs. global diffusive behavior in the higher-dimensional Keller-Segel model
- A user's guide to PDE models for chemotaxis
- Compact sets in the space \(L^ p(0,T;B)\)
- Steady-state distribution of bacteria chemotactic toward oxygen
- Measure valued solutions of the 2D Keller-Segel system
- Finite-time blow-up in the higher-dimensional parabolic-parabolic Keller-Segel system
- A new approach toward boundedness in a two-dimensional parabolic chemotaxis system with singular sensitivity
- Global existence and boundedness of radial solutions to a two dimensional fully parabolic chemotaxis system with general sensitivity
- Large-Data Global Generalized Solutions in a Chemotaxis System with Tensor-Valued Sensitivities
- Global solutions in a fully parabolic chemotaxis system with singular sensitivity
- A unified method for boundedness in fully parabolic chemotaxis systems with signal‐dependent sensitivity
- Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues
- Reduction of critical mass in a chemotaxis system by external application of chemoattractant