A unifying approach toward boundedness in Keller–Segel type cross‐diffusion systems via conditional L∞$L^\infty$ estimates for taxis gradients
From MaRDI portal
Publication:6093884
DOI10.1002/mana.202000403zbMath1525.35050OpenAlexW4294169850MaRDI QIDQ6093884
Publication date: 9 October 2023
Published in: Mathematische Nachrichten (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1002/mana.202000403
A priori estimates in context of PDEs (35B45) Cell movement (chemotaxis, etc.) (92C17) Quasilinear parabolic equations (35K59) Initial-boundary value problems for second-order parabolic systems (35K51)
Related Items
Conditional estimates in three-dimensional chemotaxis-Stokes systems and application to a Keller-Segel-fluid model accounting for gradient-dependent flux limitation, Existence and large time behavior for a Keller–Segel model with gradient dependent chemotactic sensitivity, Global boundedness in a 2D chemotaxis-Navier–Stokes system with flux limitation and nonlinear production, Global stability of a PDE-ODE model for acid-mediated tumor invasion, Boundedness in a chemotaxis-fluid system involving a gradient-dependent flux limitation and indirect signal production mechanism, Small-density solutions to Keller-Segel-Navier-Stokes system with rapidly decaying diffusivities, Global weak solutions in a three-dimensional Keller-Segel-Navier-Stokes system with gradient-dependent flux limitation, Suppressing blow-up by gradient-dependent flux limitation in a planar Keller-Segel-Navier-Stokes system, Small-density solutions in Keller-Segel systems involving rapidly decaying diffusivities, Global classical solutions in a self-consistent chemotaxis-fluid system with gradient-dependent flux limitation
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Very weak global solutions to a parabolic-parabolic chemotaxis-system with logistic source
- Boundedness and decay property in a three-dimensional Keller-Segel-Stokes system involving tensor-valued sensitivity with saturation
- Spatio-temporal models of lymphangiogenesis in wound healing
- Global bounded solutions of the higher-dimensional Keller-Segel system under smallness conditions in optimal spaces
- Global classical small-data solutions for a three-dimensional chemotaxis Navier-Stokes system involving matrix-valued sensitivities
- Locally bounded global solutions to a chemotaxis consumption model with singular sensitivity and nonlinear diffusion
- Boundedness in a quasilinear parabolic-parabolic Keller-Segel system with subcritical sensitivity
- Exponential attractor for a chemotaxis-growth system of equations
- Global existence and boundedness in a Keller-Segel-Stokes system involving a tensor-valued sensitivity with saturation: the 3D case
- A mathematical model for lymphangiogenesis in normal and diabetic wounds
- Quasilinear nonuniformly parabolic system modelling chemotaxis
- Existence and uniqueness theorem on mild solutions to the Keller-Segel system coupled with the Navier-Stokes fluid
- Aggregation vs. global diffusive behavior in the higher-dimensional Keller-Segel model
- A user's guide to PDE models for chemotaxis
- Pattern formation in a generalized chemotactic model
- Finite-time blow-up in low-dimensional Keller-Segel systems with logistic-type superlinear degradation
- How strong a logistic damping can prevent blow-up for the minimal Keller-Segel chemotaxis system?
- Traveling wave and aggregation in a flux-limited Keller-Segel model
- On a parabolic-elliptic system with gradient dependent chemotactic coefficient
- Large-time behavior of a parabolic-parabolic chemotaxis model with logarithmic sensitivity in one dimension
- When do Keller-Segel systems with heterogeneous logistic sources admit generalized solutions?
- Finite-time blow-up in a quasilinear degenerate chemotaxis system with flux limitation
- Study of a chemo-repulsion model with quadratic production. II: Analysis of an unconditionally energy-stable fully discrete scheme
- Eventual smoothness and asymptotics in a three-dimensional chemotaxis system with logistic source
- Extensibility criterion ruling out gradient blow-up in a quasilinear degenerate chemotaxis system with flux limitation
- Asymptotic stability in a fully parabolic quasilinear chemotaxis model with general logistic source and signal production
- Fluid interaction does not affect the critical exponent in a three-dimensional Keller-Segel-Stokes model
- \(L^{\gamma}\)-measure criteria for boundedness in a quasilinear parabolic-elliptic Keller-Segel system with supercritical sensitivity
- \(L^\sigma\)-measure criteria for boundedness in a quasilinear parabolic-parabolic Keller-Segel system with supercritical sensitivity
- Finite-time blow-up in the higher-dimensional parabolic-parabolic Keller-Segel system
- Boundedness in a chemotaxis system with nonlinear signal production
- Large time behavior in the logistic Keller-Segel model via maximal Sobolev regularity
- Boundedness in quasilinear Keller-Segel systems of parabolic-parabolic type on non-convex bounded domains
- Stabilization in a chemotaxis model for tumor invasion
- Blow-up in a chemotaxis model without symmetry assumptions
- A degenerate chemotaxis system with flux limitation: Maximally extended solutions and absence of gradient blow-up
- Semilinear Parabolic Problems Define Semiflows on C k Spaces
- Finite-time blow-up in a quasilinear system of chemotaxis
- Does a ‘volume-filling effect’ always prevent chemotactic collapse?
- On Explosions of Solutions to a System of Partial Differential Equations Modelling Chemotaxis
- A critical blow-up exponent in a chemotaxis system with nonlinear signal production
- Stiff-response-induced instability for chemotactic bacteria and flux-limited Keller–Segel equation
- Cross-diffusion and traveling waves in porous-media flux-saturated Keller–Segel models
- Boundedness in the Higher-Dimensional Parabolic-Parabolic Chemotaxis System with Logistic Source
- A critical blow-up exponent for flux limiation in a Keller-Segel system
- Global small-data solutions of a two-dimensional chemotaxis system with rotational flux terms
- Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues
- Finite-time blow-up in a degenerate chemotaxis system with flux limitation
- Blowup of nonradial solutions to parabolic-elliptic systems modeling chemotaxis in two-dimensional domains
- $L^1$ solutions to parabolic Keller-Segel systems involving arbitrary superlinear degradation
