Modeling multiple taxis: tumor invasion with phenotypic heterogeneity, haptotaxis, and unilateral interspecies repellence
DOI10.3934/dcdsb.2020284zbMath1467.35323arXiv2005.01444OpenAlexW3087532573MaRDI QIDQ2026618
Jonas Lenz, Christina Surulescu, Christian Stinner, Niklas Kolbe, Nikolaos Sfakianakis
Publication date: 20 May 2021
Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2005.01444
global existencenumerical simulationstumor invasioninterspecies repellencemultiple taxis and review of models
Nonlinear parabolic equations (35K55) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Cell biology (92C37) Weak solutions to PDEs (35D30) Computational methods for problems pertaining to biology (92-08) Cell movement (chemotaxis, etc.) (92C17)
Related Items (9)
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Chemotactic signaling, microglia, and Alzheimer's disease senile plaques: Is there a connection?
- On the boundedness and decay of solutions for a chemotaxis-haptotaxis system with nonlinear diffusion
- Boundedness in a multi-dimensional chemotaxis-haptotaxis model with nonlinear diffusion
- Boundedness in a three-dimensional chemotaxis-haptotaxis model
- Boundedness in a quasilinear chemotaxis-haptotaxis system with logistic source
- Nondegeneracy of blow-up points for the parabolic Keller-Segel system
- A stochastic multiscale model for acid mediated cancer invasion
- On a multiscale model involving cell contractivity and its effects on tumor invasion
- Mathematical modelling of cancer invasion: implications of cell adhesion variability for tumour infiltrative growth patterns
- Glioma follow white matter tracts: a multiscale DTI-based model
- A multiscale model of cell mobility: from a kinetic to a hydrodynamic description
- Global existence for a degenerate haptotaxis model of cancer invasion
- Boundedness in a three-dimensional chemotaxis-haptotaxis model with nonlinear diffusion
- Global existence of a two-dimensional chemotaxis-haptotaxis model with remodeling of non-diffusible attractant
- Implicit-explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxation
- A study on time discretization and adaptive mesh refinement methods for the simulation of cancer invasion: the urokinase model
- Spatial and spatio-temporal patterns in a cell-haptotaxis model
- Model for chemotaxis
- Mathematical modelling of cancer invasion of tissue: dynamic heterogeneity
- Boundedness in the higher-dimensional chemotaxis-haptotaxis model with nonlinear diffusion
- A multiscale model for glioma spread including cell-tissue interactions and proliferation
- A density-dependent chemotaxis-haptotaxis system modeling cancer invasion
- A user's guide to PDE models for chemotaxis
- Global existence of classical solutions to a combined chemotaxis-haptotaxis model with logistic source
- Model analysis of spatial patterns in mountain pine beetle outbreaks
- From 1970 until present: The Keller-Segel model in chemotaxis and its consequences. I
- Development and applications of a model for cellular response to multiple chemotactic cues
- Repulsion effects on boundedness in the higher dimensional fully parabolic attraction-repulsion chemotaxis system
- Structured models of cell migration incorporating molecular binding processes
- Large time behavior of solutions to a fully parabolic attraction-repulsion chemotaxis system with logistic source
- Singular structure formation in a degenerate haptotaxis model involving myopic diffusion
- Global weak solutions to a strongly degenerate haptotaxis model
- Mathematical modelling of cancer cell invasion of tissue: local and non-local models and the effect of adhesion
- Additive Runge-Kutta schemes for convection-diffusion-reaction equations
- On some models for cancer cell migration through tissue networks
- Spatial memory and taxis-driven pattern formation in model ecosystems
- Global boundedness to a chemotaxis-haptotaxis model with nonlinear diffusion
- Mathematical models for chemotaxis and their applications in self-organisation phenomena
- Large-data solutions in a three-dimensional chemotaxis-haptotaxis system with remodeling of non-diffusible attractant: the role of sub-linear production of diffusible signal
- Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method
- A multiscale modeling approach to glioma invasion with therapy
- A multiscale approach to the migration of cancer stem cells: mathematical modelling and simulations
- A chemotaxis-haptotaxis system with haptoattractant remodeling: boundedness enforced by mild saturation of signal production
- Mathematical model of macrophage-facilitated breast cancer cells invasion
- Boundedness in quasilinear Keller-Segel systems of parabolic-parabolic type on non-convex bounded domains
- Distributions, Sobolev spaces, elliptic equations
- Modeling complex living systems. A kinetic theory and stochastic game approach.
- Boundedness vs. blow-up in a chemotaxis system
- Modeling cell movement in anisotropic and heterogeneous network tissues
- A stochastic model featuring acid-induced gaps during tumor progression
- Boundedness in a chemotaxis–haptotaxis model with nonlinear diffusion
- Global existence for a go-or-grow multiscale model for tumor invasion with therapy
- Global Weak Solutions in a PDE-ODE System Modeling Multiscale Cancer Cell Invasion
- 'Go or Grow': the key to the emergence of invasion in tumour progression?
- A MULTISCALE APPROACH TO CELL MIGRATION IN TISSUE NETWORKS
- A quasilinear chemotaxis-haptotaxis model: The roles of nonlinear diffusion and logistic source
- A Chemotaxis-Haptotaxis Model: The Roles of Nonlinear Diffusion and Logistic Source
- On a class of multiscale cancer cell migration models: Well-posedness in less regular function spaces
- Mathematical modeling of chemotaxis and glial scarring around implanted electrodes
- A Classification of Spikes and Plateaus
- Large Time Behavior in a Multidimensional Chemotaxis-Haptotaxis Model with Slow Signal Diffusion
- A multiscale model for pH-tactic invasion with time-varying carrying capacities
- Global solution for a chemotactic–haptotactic model of cancer invasion
- Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
- Heat kernels and maximal lp—lqestimates for parabolic evolution equations
- Global classical solution and boundedness to a chemotaxis-haptotaxis model with re-establishment mechanisms
- A note for global existence of a two-dimensional chemotaxis–haptotaxis model with remodeling of non-diffusible attractant
- Global boundedness of solutions to a chemotaxis–haptotaxis model with tissue remodeling
- Higher-order models for glioma invasion: From a two-scale description to effective equations for mass density and momentum
- A strongly degenerate diffusion‐haptotaxis model of tumour invasion under the go‐or‐grow dichotomy hypothesis
- Effective equations for anisotropic glioma spread with proliferation: a multiscale approach and comparisons with previous settings
- CONVERGENCE OF A CANCER INVASION MODEL TO A LOGISTIC CHEMOTAXIS MODEL
- Asymptotic behavior of solutions to a tumor angiogenesis model with chemotaxis–haptotaxis
- A Hybrid Multiscale Model for Cancer Invasion of the Extracellular Matrix
- A new result for 2D boundedness of solutions to a chemotaxis–haptotaxis model with/without sub-logistic source
- Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues
- On a structured multiscale model for acid-mediated tumor invasion: The effects of adhesion and proliferation
- GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR OF A TUMOR ANGIOGENESIS MODEL WITH CHEMOTAXIS AND HAPTOTAXIS
- MODEL HIERARCHIES FOR CELL AGGREGATION BY CHEMOTAXIS
- MATHEMATICAL MODELLING OF CANCER CELL INVASION OF TISSUE: THE ROLE OF THE UROKINASE PLASMINOGEN ACTIVATION SYSTEM
- Large time behavior of solution to a fully parabolic chemotaxis-haptotaxis model in higher dimensions
This page was built for publication: Modeling multiple taxis: tumor invasion with phenotypic heterogeneity, haptotaxis, and unilateral interspecies repellence