A Degenerate Cross-Diffusion System as the Inviscid Limit of a Nonlocal Tissue Growth Model
From MaRDI portal
Publication:6195329
DOI10.1137/23m1575573arXiv2303.10620OpenAlexW4330338873MaRDI QIDQ6195329
Noemi David, Unnamed Author, Tomasz Dębiec, Markus Schmidtchen
Publication date: 13 March 2024
Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2303.10620
Stability in context of PDEs (35B35) Reaction-diffusion equations (35K57) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Degenerate parabolic equations (35K65) Applications of operator theory in chemistry and life sciences (47N60) Second-order parabolic systems (35K40) Quasilinear parabolic equations (35K59)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations
- Nonlinear degenerate cross-diffusion systems with nonlocal interaction
- Mathematical modeling of collective behavior in socio-economic and life sciences
- Epidemic models with spatial spread due to population migration
- On interacting populations that disperse to avoid crowding: preservation of segregation
- On a degenerate diffusion equation of the form \(c(z)_ t=\phi (z_ x)_ x\) with application to population dynamics
- A non-local model for a swarm
- Adhesion and volume constraints via nonlocal interactions determine cell organisation and migration profiles
- On nonlinear cross-diffusion systems: an optimal transport approach
- A blob method for diffusion
- Compactness for nonlinear continuity equations
- Incompressible limit for a two-species tumour model with coupling through Brinkman's law in one dimension
- A cross-diffusion system obtained via (convex) relaxation in the JKO scheme
- Existence and regularity for a system of porous medium equations with small cross-diffusion and nonlocal drifts
- Segregation effects and gap formation in cross-diffusion models
- Global existence theorem for a model governing the motion of two cell populations
- Incompressible limit for a two-species model with coupling through Brinkman's law in any dimension
- Hele-Shaw limit for a system of two reaction-(Cross-)diffusion equations for living tissues
- A nonlinear parabolic-hyperbolic system for contact inhibition and a degenerate parabolic Fisher-KPP equation
- Individual-based and continuum models of growing cell populations: a comparison
- On a cross-diffusion model for multiple species with nonlocal interaction and size exclusion
- A population dynamics model of cell-cell adhesion incorporating population pressure and density saturation
- The Hele-Shaw asymptotics for mechanical models of tumor growth
- On a cross-diffusion segregation problem arising from a model of interacting particles
- Continuous models for cell-cell adhesion
- Darcy's law with a source term
- Une méthode particulaire déterministe pour des équations diffusives non linéaires
- Incompressible limit of a mechanical model of tumour growth with viscosity
- A Deterministic Approximation of Diffusion Equations Using Particles
- A note on interacting populations that disperse to avoid crowding
- Existence and Incompressible Limit of a Tissue Growth Model with Autophagy
- On interacting populations that disperse to avoid crowding: the case of equal dispersal velocities
- Splitting Schemes and Segregation in Reaction Cross-Diffusion Systems
- Travelling wave solutions of a parabolic-hyperbolic system for contact inhibition of cell-growth
- Diffusion of Particles with Short-Range Interactions
- Zoology of a Nonlocal Cross-Diffusion Model for Two Species
- Trend to equilibrium for systems with small cross-diffusion
- Coarse graining of a Fokker–Planck equation with excluded volume effects preserving the gradient flow structure
- Aggregation-Diffusion Equations: Dynamics, Asymptotics, and Singular Limits
- Nonlinear Cross-Diffusion with Size Exclusion
- A two-species hyperbolic–parabolic model of tissue growth
- The boundedness-by-entropy method for cross-diffusion systems
- A tumor growth model of Hele-Shaw type as a gradient flow
- A free boundary problem arising in a simplified tumour growth model of contact inhibition
- Phenotypic heterogeneity in a model of tumour growth: existence of solutions and incompressible limit
This page was built for publication: A Degenerate Cross-Diffusion System as the Inviscid Limit of a Nonlocal Tissue Growth Model
