Existence of Solutions to Reaction Cross Diffusion Systems

DOI10.1137/22m1497742zbMath1527.35187arXiv2107.12412OpenAlexW3186543169MaRDI QIDQ6090029

Matthew Jacobs

Publication date: 13 November 2023

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2107.12412

zbMATH Keywords

reaction-diffusion equationconvex dualityhyperbolic-parabolic systemcell growth modelenergy dissipation relation

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Duality theory (optimization) (49N15) Initial value problems for PDEs of mixed type (35M11)

Cites Work

• Congestion-driven dendritic growth
• A two-phase model of solid tumour growth
• On nonlinear cross-diffusion systems: an optimal transport approach
• Global existence theorem for a model governing the motion of two cell populations
• Interface dynamics in a two-phase tumor growth model
• Hele-Shaw limit for a system of two reaction-(Cross-)diffusion equations for living tissues
• Multiphase modelling of tumour growth and extracellular matrix interaction: mathematical tools and applications
• The Hele-Shaw asymptotics for mechanical models of tumor growth
• Darcy's law with a source term
• THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION
• Incompressible limit of a mechanical model of tumour growth with viscosity
• Existence and Incompressible Limit of a Tissue Growth Model with Autophagy
• Splitting Schemes and Segregation in Reaction Cross-Diffusion Systems
• A two-species hyperbolic–parabolic model of tissue growth
• Quasi-static evolution and congested crowd transport
• Convex analysis and monotone operator theory in Hilbert spaces
• Unnamed Item