On a nonlinear model for tumor growth: global in time weak solutions

DOI10.1007/s00021-014-0180-7zbMath1307.35191arXiv1408.4606OpenAlexW1994414140MaRDI QIDQ2257393

Donatella Donatelli, Konstantina Trivisa

Publication date: 25 February 2015

Published in: Journal of Mathematical Fluid Mechanics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1408.4606

zbMATH Keywords

existencepenalizationmixed modelsmoving domaincancer progressiontumor growth models

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Navier-Stokes equations (35Q30) Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics (76N10)

Related Items

Global Weak Solutions of PDEs for Compressible Media: A Compactness Criterion to Cover New Physical Situations ⋮ On a nonlinear model for tumor growth in a cellular medium ⋮ Incompressible limit for a two-species model with coupling through Brinkman's law in any dimension ⋮ Convergence of the marker-and-cell scheme for the semi-stationary compressible Stokes problem ⋮ On a nonlinear model for tumor growth: global in time weak solutions ⋮ On a Fluid-Particle Interaction Model: Global in Time Weak Solutions Within a Moving Domain in $$\mathbb{R}^{3}$$ ⋮ Existence results for a monophasic compressible Darcy-Brinkman's flow in porous media ⋮ Weak solutions for the Stokes system for compressible fluids with general pressure

Cites Work

• Unnamed Item
• Unnamed Item
• Convergence of a Brinkman-type penalization for compressible fluid flows
• The Navier-Stokes equations. An elementary functional analytic approach
• Continuation techniques for a penalty approximation of the Navier-Stokes equations
• From the dynamics of gaseous stars to the incompressible Euler equations
• Penalty finite element method for the Navier-Stokes equations
• Penalty approximation of Stokes flow
• A hierarchy of cancer models and their mathematical challenges
• Weak solutions to the barotropic Navier-Stokes system with slip boundary conditions in time dependent domains
• Level set methods and dynamic implicit surfaces
• A two-phase free boundary problem with discontinuous velocity: Application to tumor model
• Hypoxia inducible factors-mediated inhibition of cancer by GM-CSF: a mathematical model
• Monotone iterative technique for first-order nonlinear periodic boundary value problems on time scales
• On a nonlinear model for tumor growth: global in time weak solutions
• On the motion of a viscous compressible radiative-reacting gas
• Local behavior of solutions of quasilinear parabolic equations
• Mathematical Models of Avascular Tumor Growth