A quasilinear chemotaxis-haptotaxis system: existence and blow-up results

Reaction-diffusion equations (35K57) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Cell movement (chemotaxis, etc.) (92C17) Blow-up in context of PDEs (35B44) Initial-boundary value problems for PDEs of mixed type (35M13) Quasilinear parabolic equations (35K59)

Cites Work

Title not available (Why is that?)
Title not available (Why is that?)
Title not available (Why is that?)
Title not available (Why is that?)
Title not available (Why is that?)
Title not available (Why is that?)
Title not available (Why is that?)
Boundedness in a three-dimensional chemotaxis-haptotaxis model
Boundedness in a quasilinear chemotaxis-haptotaxis system with logistic source
Finite-time blowup and global-in-time unbounded solutions to a parabolic-parabolic quasilinear Keller-Segel system in higher dimensions
Nondegeneracy of blow-up points for the parabolic Keller-Segel system
Boundedness in a fully parabolic chemotaxis system with singular sensitivity
Global bounded solutions of the higher-dimensional Keller-Segel system under smallness conditions in optimal spaces
Application of an Adams type inequality to a two-chemical substances chemotaxis system
Boundedness in a quasilinear parabolic-parabolic Keller-Segel system with subcritical sensitivity
Hölder estimates for local solutions of some doubly nonlinear degenerate parabolic equations
Initiation of slime mold aggregation viewed as an instability
Finite time blow-up for a one-dimensional quasilinear parabolic-parabolic chemotaxis system
Mathematical modelling of cancer invasion of tissue: dynamic heterogeneity
Boundedness in the higher-dimensional chemotaxis-haptotaxis model with nonlinear diffusion
Aggregation vs. global diffusive behavior in the higher-dimensional Keller-Segel model
A user's guide to PDE models for chemotaxis
From 1970 until present: The Keller-Segel model in chemotaxis and its consequences. I
Global classical solvability and generic infinite-time blow-up in quasilinear Keller-Segel systems with bounded sensitivities
From 1970 until present: the Keller-Segel model in chemotaxis and its consequences. II
Blow-up profiles and life beyond blow-up in the fully parabolic Keller-Segel system
Asymptotic stability in a quasilinear chemotaxis-haptotaxis model with general logistic source and nonlinear signal production
Keller-Segel chemotaxis models: a review
Boundedness in a quasilinear chemotaxis-haptotaxis model of parabolic-parabolic-ODE type
Large time behavior in a quasilinear chemotaxis model with indirect signal absorption
Finite time blow-up in the higher dimensional parabolic-elliptic-ODE minimal chemotaxis-haptotaxis system
Infinite time blow-up of many solutions to a general quasilinear parabolic-elliptic Keller-Segel system
New critical exponents in a fully parabolic quasilinear Keller-Segel system and applications to volume filling models
\(L^{\gamma}\)-measure criteria for boundedness in a quasilinear parabolic-elliptic Keller-Segel system with supercritical sensitivity
Finite-time blow-up in quasilinear parabolic-elliptic chemotaxis system with nonlinear signal production
Finite-time blow-up in the higher-dimensional parabolic-parabolic Keller-Segel system
Finite-time blowup in a supercritical quasilinear parabolic-parabolic Keller-Segel system in dimension 2
Boundedness in quasilinear Keller-Segel systems of parabolic-parabolic type on non-convex bounded domains
Boundedness vs. blow-up in a chemotaxis system
Global weak solutions of a parabolic-elliptic Keller-Segel system with gradient dependent chemotactic coefficients
Critical mass in a quasilinear parabolic-elliptic Keller-Segel model
Boundedness and stabilization in a multi-dimensional chemotaxis—haptotaxis model
On the martingale problem for degenerate-parabolic partial differential operators with unbounded coefficients and a mimicking theorem for Itô processes
A Chemotaxis-Haptotaxis Model: The Roles of Nonlinear Diffusion and Logistic Source
Large Time Behavior in a Multidimensional Chemotaxis-Haptotaxis Model with Slow Signal Diffusion
Finite-time blow-up in a quasilinear system of chemotaxis
A Combined Chemotaxis-haptotaxis System: The Role of Logistic Source
Does a ‘volume-filling effect’ always prevent chemotactic collapse?
L^PBounds of solutions of reaction-diffusion equations
Global Behaviour of a Reaction-Diffusion System Modelling Chemotaxis
Heat kernels and maximal l^p—l^qestimates for parabolic evolution equations
Global classical solution and boundedness to a chemotaxis-haptotaxis model with re-establishment mechanisms
A sufficient condition of sensitivity functions for boundedness of solutions to a parabolic-parabolic chemotaxis system
Chemotactic Aggregation versus Logistic Damping on Boundedness in the 3D Minimal Keller--Segel Model
CONVERGENCE OF A CANCER INVASION MODEL TO A LOGISTIC CHEMOTAXIS MODEL
Single-point blow-up in the Cauchy problem for the higher-dimensional Keller–Segel system
Global solvability and stabilization to a cancer invasion model with remodelling of ECM
Negligibility of haptotaxis effect in a chemotaxis–haptotaxis model
Boundedness of solutions to parabolic-elliptic Keller-Segel systems with signal-dependent sensitivity
Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues
MATHEMATICAL MODELLING OF CANCER CELL INVASION OF TISSUE: THE ROLE OF THE UROKINASE PLASMINOGEN ACTIVATION SYSTEM
Classical solutions to Cauchy problems for parabolic-elliptic systems of Keller-Segel type
Finite time blow-up in a parabolic-elliptic Keller-Segel system with flux dependent chemotactic coefficient
A family of mass‐critical Keller–Segel systems
A Result on Parabolic Gradient Regularity in Orlicz Spaces and Application to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type Cross-Diffusion System

This page was built for publication: A quasilinear chemotaxis-haptotaxis system: existence and blow-up results

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6584922)