Preventing blow-up in a chemotaxis model

No abstract is available for this paper.

• Publication year

  2005

• Venue

  Journal of Mathematical Analysis and Applications

• Publication date

  2005-05-15

• Fields of study

  Mathematics

• Identifiers
  DOI 10.1016/J.JMAA.2004.12.009
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Global Solutions of Some Chemotaxis and Angiogenesis Systems in High Space Dimensions

  2004cited by this paper
• On the stability of homogeneous solutions to some aggregation models

  2003cited by this paper
• Percolation, morphogenesis, and burgers dynamics in blood vessels formation.

  2003cited by this paper
• Modeling the early stages of vascular network assembly

  2003cited by this paper
• ON THE CLOSURE OF MASS BALANCE MODELS FOR TUMOR GROWTH

  2002cited by this paper
• Nonlinear parabolic differential equations and inequalities

  2002cited by this paper
• Lyapunov functions and $L^{p}$-estimates for a class of reaction-diffusion systems

  2001cited by this paper
• Global Existence for a Parabolic Chemotaxis Model with Prevention of Overcrowding

  2001cited by this paper
• Partial Differential Equations

  1999cited by this paper
• Global Behaviour of a Reaction‐Diffusion System Modelling Chemotaxis

  1998cited by this paper
• LOCAL AND GLOBAL SOLVABILITY OF SOME PARABOLIC SYSTEMS MODELLING CHEMOTAXIS

  1998cited by this paper
• A blow-up mechanism for a chemotaxis model

  1997cited by this paper
• Singularity patterns in a chemotaxis model

  1996cited by this paper
• Chemotactic collapse for the Keller-Segel model

  1996cited by this paper
• On explosions of solutions to a system of partial differential equations modelling chemotaxis

  1992cited by this paper
• Elliptic Problems in Nonsmooth Domains

  1985cited by this paper
• Chemotactic Collapse in Two Dimensions

  1984cited by this paper
• Nonlinear aspects of chemotaxis

  1981cited by this paper
• LP Bounds of solutions of reaction-diffusion equations

  1979cited by this paper
• Chemotaxis, signal relaying and aggregation morphology.

  1973cited by this paper
• Initiation of slime mold aggregation viewed as an instability.

  1970cited by this paper

• Chemotactic Feedback Controls Patterning in Hybrid Tumor--Stroma Model

  2026cites this paper
• Global boundedness and bifurcation of a diffusive predator-prey model with fear effect and prey-taxis

  2026cites this paper
• Mode-Wise Spectral Criteria for Coupled Mass Transport in Hybrid PDE--ODE Tumor Microenvironments

  2026cites this paper
• Convergence of a finite volume scheme for a model for ants

  2025influential citation
• Finite-time blow-up on a volume-filling attraction–repulsion system

  2025cites this paper
• A class of models with a nonlinear indirect chase-and-escape effect

  2025cites this paper
• A new result for global solvability to a two-dimensional Keller-Segel(-Navier)-Stokes system with indirect signal production

  2025cites this paper
• Global existence in a 2D Keller–Segel–Navier–Stokes system with indirect signal production

  2025influential citation
• Global existence in a three-dimensional chemotaxis-Stokes system with p-Laplacian diffusion and singular sensitivity

  2025cites this paper
• Global weak solutions to a chemotaxis system for virus dynamics with $ p $-Laplacian diffusion and singular sensitivity

  2025cites this paper
• Global Classical Solutions to a Predator-Prey Model with Nonlinear Indirect Chemotaxis Mechanism

  2024influential citation
• Global boundedness for a predator-prey model with nonlinear indirect pursuit-evasion effect

  2024cites this paper
• Aggregation-diffusion phenomena: from microscopic models to free boundary problems

  2024cites this paper
• Localization of Solutions to Equations of Tumor Dynamics

  2024cites this paper
• Lane Formation and Aggregation Spots in a Model of Ants

  2024influential citation
• Radial blow-up in quasilinear Keller-Segel systems: approaching the full picture

  2024influential citation
• Global bounded solution of a 3D chemotaxis-Stokes system with slow $ p $-Laplacian diffusion and logistic source

  2024cites this paper
• The effects of cross-diffusion and logistic source on the boundedness of solutions to a pursuit-evasion model

  2023cites this paper
• Global Boundedness of Solutions to a Quasilinear Chemotaxis System with Nonlocal Nonlinear Reaction

  2023influential citation
• A semigroup approach to a reaction–diffusion system with cross-diffusion

  2023cites this paper
• Global boundedness for a chemotaxis system involving nonlinear indirect consumption mechanism

  2023cites this paper
• Some further progress for boundedness of solutions to a quasilinear higher–dimensional chemotaxis–haptotaxis model with nonlinear diffusion

  2023cites this paper
• Hele-Shaw flow as a singular limit of a Keller-Segel system with nonlinear diffusion

  2023influential citation
• Depleting the signal: Analysis of chemotaxis‐consumption models—A survey

  2023cites this paper
• Global boundedness in an attraction-repulsion chemotaxis system involving nonlinear indirect signal mechanism

  2023cites this paper
• Boundedness criteria for the quasilinear attraction-repulsion chemotaxis system with nonlinear signal production and logistic source

  2022cites this paper
• A new result for global solvability to a two-dimensional attraction-repulsion Navier-Stokes system with consumption of chemoattractant

  2022cites this paper
• Global Existence, Regularity and Boundedness in a Higher-dimensional Chemotaxis-Navier-Stokes System with Nonlinear Diffusion and General Sensitivity

  2022cites this paper
• Eventual smoothness and stabilization in a three-dimensional Keller–Segel–Navier–Stokes system with rotational flux

  2022cites this paper
• On the fast spreading scenario

  2021cites this paper
• Global existence and boundedness in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion and general sensitivity

  2021cites this paper
• Global solvability of prey–predator models with indirect predator-taxis

  2021cites this paper
• Existence of weak solutions for porous medium equation with a divergence type of drift term

  2021cites this paper
• Multiscale Convergence of the Inverse Problem for Chemotaxis in the Bayesian Setting

  2021cites this paper
• A novel nonlocal partial differential equation model of endothelial progenitor cell cluster formation during the early stages of vasculogenesis.

  2021cites this paper
• Global existence and boundedness in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion and general sensitivity

  2021cites this paper
• Continuity results for degenerate diffusion equations with LtpLxq drifts

  2021cites this paper
• Boundedness in a chemotaxis-fluid system involving a saturated sensitivity and indirect signal production mechanism

  2021cites this paper
• Dissipation enhancement of planar helical flows and applications to three-dimensional Kuramoto-Sivashinsky and Keller-Segel equations

  2021cites this paper
• Global solvability of prey–predator models with indirect predator-taxis

  2021cites this paper
• A blow-up result for the chemotaxis system with nonlinear signal production and logistic source

  2021cites this paper
• A reducing mechanism on wave speed for chemotaxis systems with degenerate diffusion

  2020cites this paper
• Boundedness of weak solutions of a chemotaxis-Stokes system with slow p-Laplacian diffusion

  2020cites this paper
• Global well-posedness for the primitive equations coupled to nonlinear moisture dynamics with phase changes

  2020cites this paper
• Global solvability in a two-dimensional self-consistent chemotaxis-Navier-Stokes system

  2020cites this paper
• Relaxed parameter conditions for chemotactic collapse in logistic-type parabolic–elliptic Keller–Segel systems

  2020cites this paper
• On the $8\pi$-subcritical mass threshold of a Patlak-Keller-Segel-Navier-Stokes system

  2020cites this paper
• Continuity results for degenerate diffusion equations with $L^{p}_t L^{q}_{x}$ drifts

  2019cites this paper
• Large time behavior of solutions to a fully parabolic chemotaxis–haptotaxis model in N dimensions

  2019cites this paper
• Vanishing cross-diffusion limit in a Keller–Segel system with additional cross-diffusion

  2019cites this paper
• L-MEASURE CRITERIA FOR BOUNDEDNESS IN A QUASILINEAR PARABOLIC-ELLIPTIC KELLER-SEGEL SYSTEM WITH SUPERCRITICAL SENSITIVITY

  2019cites this paper
• Numerical Simulations for Chemotaxis Models

  2019cites this paper
• Phase Transitions and Bump Solutions of the Keller-Segel Model with Volume Exclusion

  2019cites this paper
• Global existence and boundedness in a chemotaxis‐Stokes system with arbitrary porous medium diffusion

  2019cites this paper
• Uniform-in-time bounds for approximate solutions of the drift–diffusion system

  2019cites this paper
• Cellular Potts Models

  2019cites this paper
• Global existence and uniqueness of solutions to a chemotaxis system

  2019cites this paper
• Discontinuous phase transition in chemotactic aggregation with density-dependent pressure.

  2019cites this paper
• An optimal result for global classical and bounded solutions in a two-dimensional Keller-Segel-Navier-Stokes system with sensitivity

  2019influential citation
• Large-time asymptotics for a matrix spin drift-diffusion model

  2019cites this paper
• Mathematical Research for Models Which is Related to Chemotaxis System

  2019cites this paper
• Solvability and numerical simulations for tumor invasion model with nonlinear diffusion

  2019cites this paper
• Global existence, smooth and stabilization in a three-dimensional Keller-Segel-Navier-Stokes system with rotational flux

  2019cites this paper
• Vanishing cross-diffusion limit in a Keller-Segel system with additional cross-diffusion

  2019cites this paper
• Global well-posedness for the primitive equations coupled to nonlinear moisture dynamics with phase changes

  2019cites this paper
• Minimal models of invasion and clonal selection in cancer

  2018cites this paper
• Pattern formation for a nonlinear diffusion chemotaxis model with logistic source

  2018influential citation
• A SURVEY ON WELL-BALANCED AND ASYMPTOTIC PRESERVING SCHEMES FOR HYPERBOLIC MODELS FOR CHEMOTAXIS

  2018cites this paper
• On a class of diffusion-aggregation equations

  2018cites this paper
• Global existence and boundedness of weak solutions to a chemotaxis–Stokes system with rotational flux term

  2018cites this paper
• Global classical solutions in a two-dimensional chemotaxis-Navier-Stokes system with subcritical sensitivity

  2018cites this paper
• MIXING, FLOCKING AND COOPERATION: ANALYTICAL STUDIES OF TRANSPORT PHENOMENA IN BIOLOGY

  2018cites this paper
• A blow-up result for a quasilinear chemotaxis system with logistic source in higher dimensions

  2018cites this paper
• Boundedness and large time behavior in a quasilinear chemotaxis model for tumor invasion

  2018cites this paper
• Global weak solutions in a three-dimensional Keller–Segel–Navier–Stokes system with nonlinear diffusion

  2017cites this paper
• Global existence and boundedness in a 3D Keller–Segel–Stokes system with nonlinear diffusion and rotational flux

  2017cites this paper
• Microscopic derivation of the Keller-Segel equation in the sub-critical regime

  2017cites this paper
• Global existence and boundedness in a 3D Keller–Segel–Stokes system with nonlinear diffusion and rotational flux

  2017cites this paper
• A biophysical model of tumor invasion

  2017cites this paper
• Global boundedness in a quasilinear chemotaxis system with general density-signal governed sensitivity ☆

  2017cites this paper
• Blow-up prevention by a three-dimensional Keller-Segel-Navier-Stokes system with nonlinear diffusion

  2017influential citation
• Uniform $$L^{\infty }$$ Estimates for Approximate Solutions of the Bipolar Drift-Diffusion System

  2017cites this paper
• On a stochastic particle model of the Keller-Segel equation and its macroscopic limit

  2017cites this paper
• A quasilinear chemotaxis–haptotaxis model: The roles of nonlinear diffusion and logistic source

  2017cites this paper
• Existence of global bounded classical solution to a quasilinear attraction–repulsion chemotaxis system with logistic source

  2017cites this paper
• Global existence and slow grow-up in a quasilinear Keller–Segel system with exponentially decaying diffusivity

  2017cites this paper
• Global Very Weak Solutions to a Chemotaxis-Fluid System with Nonlinear Diffusion

  2017cites this paper
• Global weak solutions in a three-dimensional Keller–Segel–Navier–Stokes system with subcritical sensitivity

  2017cites this paper
• Uniform L ∞ estimates for approximate solutions of the bipolar drift-diffusion system

  2017cites this paper
• Free energy of a chemotactic model with nonlinear diffusion

  2017cites this paper
• Regularity Properties of Degenerate Diffusion Equations with Drifts

  2017influential citation
• Boundedness in a quasilinear fully parabolic Keller–Segel system with logistic source

  2017cites this paper
• On the existence of weak solutions of nonlinear degenerate parabolic system with variable exponents

  2017cites this paper
• Uniform in Time L∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$L^{\infty }$\end{document}-Estimates for Nonlinear Ag

  2017cites this paper
• Mathematical modeling and its analysis for instability of the immune system induced by chemotaxis

  2017cites this paper
• Uniqueness theorem on weak solutions to the Keller–Segel system of degenerate and singular types

  2016cites this paper
• Suppression of Blow-Up in Patlak-Keller-Segel Via Shear Flows

  2016cites this paper
• A mathematical model for the simulation of the contraction of burns

  2016cites this paper
• Compactly supported stationary states of the degenerate Keller-Segel system in the diffusion-dominated regime

  2016cites this paper
• Stationary solutions with vacuum for a one-dimensional chemotaxis model with non-linear pressure

  2016cites this paper