Biological modeling with nonlocal advection–diffusion equations
From MaRDI portal
Publication:6125052
DOI10.1142/s0218202524400025arXiv2307.14396OpenAlexW4387771233MaRDI QIDQ6125052
Jonathan R. Potts, Kevin J. Painter, Thomas Hillen
Publication date: 11 April 2024
Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2307.14396
PDEs in connection with biology, chemistry and other natural sciences (35Q92) Ecology (92D40) Cell movement (chemotaxis, etc.) (92C17) Animal behavior (92D50) Research exposition (monographs, survey articles) pertaining to biology (92-02)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Home range formation in wolves due to scent marking
- A nonlocal continuum model for biological aggregation
- The mathematics behind biological invasions
- Mathematical modelling of cancer invasion: implications of cell adhesion variability for tumour infiltrative growth patterns
- Symmetries and pattern formation in hyperbolic versus parabolic models of self-organised aggregation
- Existence and uniqueness of solutions to an aggregation equation with degenerate diffusion
- A new model for self-organized dynamics and its flocking behavior
- Cellular automaton modeling of biological pattern formation. Characterization, applications, and analysis. With a foreword by Philip K. Maini
- Models of dispersal in biological systems
- Continuous models for cell migration in tissues and applications to cell sorting via differential chemotaxis
- Adding adhesion to a chemical signaling model for somite formation
- Initiation of slime mold aggregation viewed as an instability
- Pattern formation of scale cells in lepidoptera by differential origin-dependent cell adhesion
- A nonlocal model for contact attraction and repulsion in heterogeneous cell populations
- Territorial pattern formation in the absence of an attractive potential
- A user's guide to PDE models for chemotaxis
- A one-dimensional model of cell diffusion and aggregation, incorporating volume filling and cell-to-cell adhesion
- A spatially discrete model for aggregating populations
- A non-local model for a swarm
- Pattern formation in generalized Turing systems. I: Steady-state patterns in systems with mixed boundary conditions
- Modelling the role of cell-cell adhesion in the growth and development of carcinomas
- Nonlinear simulation of tumor growth
- Localization in lattice and continuum models of reinforced random walks
- Mathematical biology. Vol. 2: Spatial models and biomedical applications.
- A mathematical model for pattern formation of glioma cells outside the tumor spheroid core
- Computational approaches and analysis for a spatio-structural-temporal invasive carcinoma model
- Adhesion and volume constraints via nonlocal interactions determine cell organisation and migration profiles
- A space-jump derivation for non-local models of cell-cell adhesion and non-local chemotaxis
- The impact of adhesion on cellular invasion processes in cancer and development
- Non-local models for the formation of hepatocyte-stellate cell aggregates
- Hyperbolic and kinetic models for self-organised biological aggregations. A modelling and pattern formation approach
- An interacting particle system modelling aggregation behavior: from individuals to populations
- Patient-calibrated agent-based modelling of ductal carcinoma in situ (DCIS): from microscopic measurements to macroscopic predictions of clinical progression
- Mathematical modelling of cancer cell invasion of tissue: local and non-local models and the effect of adhesion
- Three-dimensional multispecies nonlinear tumor growth. I: Model and numerical method
- A 3-D model used to explore how cell adhesion and stiffness affect cell sorting and movement in multicellular systems
- The symmetry perspective. From equilibrium to chaos in phase space and physical space
- Spatial memory and taxis-driven pattern formation in model ecosystems
- Leadership through influence: what mechanisms allow leaders to steer a swarm?
- A novel nonlocal partial differential equation model of endothelial progenitor cell cluster formation during the early stages of vasculogenesis
- Detecting minimum energy states and multi-stability in nonlocal advection-diffusion models for interacting species
- A continuum approach to modelling cell-cell adhesion
- Nonlocal and local models for taxis in cell migration: a rigorous limit procedure
- Long-time behaviour and phase transitions for the McKean-Vlasov equation on the torus
- Nonlinear simulations of solid tumor growth using a mixture model: invasion and branching
- Consensus convergence with stochastic effects
- Modeling opinion dynamics: theoretical analysis and continuous approximation
- Mathematical model of macrophage-facilitated breast cancer cells invasion
- A continuum approximation to an off-lattice individual-cell based model of cell migration and adhesion
- A population dynamics model of cell-cell adhesion incorporating population pressure and density saturation
- On an aggregation model with long and short range interactions
- Some global results for nonlinear eigenvalue problems
- Bifurcation from simple eigenvalues
- Continuous models for cell-cell adhesion
- Modeling the morphodynamic galectin patterning network of the developing avian limb skeleton
- Phase transitions for nonlinear nonlocal aggregation-diffusion equations
- The force of cell-cell adhesion in determining the outcome in a nonlocal advection diffusion model of wound healing
- Bifurcation analysis of critical values for wound closure outcomes in wound healing experiments
- Open problems in PDE models for knowledge-based animal movement via nonlocal perception and cognitive mapping
- A nonlocal swarm model for predators–prey interactions
- Transport and Anisotropic Diffusion Models for Movement in Oriented Habitats
- Random walk with persistence and external bias
- Heterophilious Dynamics Enhances Consensus
- Existence and Asymptotic Properties of Solutions of a Nonlocal Evolution Equation Modeling Cell-Cell Adhesion
- MATHEMATICAL MODELLING OF CANCER INVASION: THE IMPORTANCE OF CELL–CELL ADHESION AND CELL–MATRIX ADHESION
- Particle, kinetic, and hydrodynamic models of swarming
- Swarm dynamics and equilibria for a nonlocal aggregation model
- Asymptotic Behavior for a Nonlinear Degenerate Diffusion Equation in Population Dynamics
- A non-local evolution equation model of cell–cell adhesion in higher dimensional space
- Aggregation, Blowup, and Collapse: The ABC's of Taxis in Reinforced Random Walks
- Pattern formation with a conservation law
- Sorting Phenomena in a Mathematical Model For Two Mutually Attracting/Repelling Species
- Global solvability and explicit bounds for non-local adhesion models
- The chemical basis of morphogenesis
- Aggregation and travelling wave dynamics in a two-population model of cancer cell growth and invasion
- Zoology of a Nonlocal Cross-Diffusion Model for Two Species
- Aggregation under local reinforcement: From lattice to continuum
- Towards a mathematical theory of behavioral human crowds
- Noisy bounded confidence models for opinion dynamics: the effect of boundary conditions on phase transitions
- Chemotaxis and cross-diffusion models in complex environments: Models and analytic problems toward a multiscale vision
- Local and Global Existence for Nonlocal Multispecies Advection-Diffusion Models
- On the approximation and efficient evaluation of integral terms in PDE models of cell adhesion
- Nonlocal Adhesion Models for Microorganisms on Bounded Domains
- Nonparametric inference of interaction laws in systems of agents from trajectory data
- Emergent Behavior in Flocks
- Mathematical modelling of cancer invasion: The multiple roles of TGF-β pathway on tumour proliferation and cell adhesion
- Pattern formation outside of equilibrium
- A Finite-Volume Method for Nonlinear Nonlocal Equations with a Gradient Flow Structure
- Complex spatial group patterns result from different animal communication mechanisms
- Local and Global Existence for an Aggregation Equation
- Boundedness of solutions of a non-local reaction–diffusion model for adhesion in cell aggregation and cancer invasion
- Non-Local Cell Adhesion Models
- Human behavioral crowds review, critical analysis and research perspectives
