Analysis of a new multispecies tumor growth model coupling 3D phase-fields with a 1D vascular network
From MaRDI portal
Publication:2066556
DOI10.1016/j.nonrwa.2021.103331zbMath1480.92046arXiv2006.10477OpenAlexW3035967161MaRDI QIDQ2066556
Prashant K. Jha, J. Tinsley Oden, Marvin Fritz, Tobias Köppl, Barbara I. Wohlmuth
Publication date: 14 January 2022
Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2006.10477
Galerkin methodtumor growthexistence of weak solutionsenergy inequalityECM degradation3D-1D coupled blood flow models
Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Free boundary problems for PDEs (35R35) Physiological flow (92C35) Pathology, pathophysiology (92C32)
Related Items
Existence of weak solutions to multiphase Cahn–Hilliard–Darcy and Cahn–Hilliard–Brinkman models for stratified tumor growth with chemotaxis and general source terms, Tumor evolution models of phase-field type with nonlocal effects and angiogenesis, A high-accuracy framework for phase-field fracture interface reconstructions with application to Stokes fluid-filled fracture surrounded by an elastic medium, Residual-based error corrector operator to enhance accuracy and reliability of neural operator surrogates of nonlinear variational boundary-value problems, Modeling and simulation of vascular tumors embedded in evolving capillary networks, Goal-oriented a-posteriori estimation of model error as an aid to parameter estimation
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Linear functional analysis. An application-oriented introduction. Translated from the 6th German edition by Robert Nürnberg
- Optimal order finite element approximation for a hyperbolic integro-differential equation
- Toward predictive multiscale modeling of vascular tumor growth, computational and experimental oncology for tumor prediction
- Global existence for a haptotaxis model of cancer invasion with tissue remodeling
- The Cahn-Hilliard equation with logarithmic potentials
- Existence and regularity of very weak solutions of the stationary Navier-Stokes equations
- Applied functional analysis. Functional analysis, Sobolev spaces and elliptic differential equations
- Necessary and sufficient conditions for the chain rule in \(W_{\text{loc}}^{1,1} (\mathbb R^N;\mathbb R^d)\) and \(BV_{\text{loc}}(\mathbb R^N;\mathbb R^d)\)
- Compact sets in the space \(L^ p(0,T;B)\)
- Continuous and discrete mathematical models of tumor-induced angiogenesis
- Three-dimensional multispecies nonlinear tumor growth. II: Tumor invasion and angiogenesis
- Three-dimensional multispecies nonlinear tumor growth. I: Model and numerical method
- On a multi-species Cahn-Hilliard-Darcy tumor growth model with singular potentials
- Phase-field model of vascular tumor growth: three-dimensional geometry of the vascular network and integration with imaging data
- Selection and validation of predictive models of radiation effects on tumor growth based on noninvasive imaging data
- Full-scale, three-dimensional simulation of early-stage tumor growth: the onset of malignancy
- Global weak solutions and asymptotic limits of a Cahn-Hilliard-Darcy system modelling tumour growth
- Nonlinear simulations of solid tumor growth using a mixture model: invasion and branching
- Well-posedness and long-time behavior of a non-autonomous Cahn-Hilliard-Darcy system with mass source modeling tumor growth
- Simulation of angiogenesis in a multiphase tumor growth model
- Energy-type estimates and global solvability in a two-dimensional chemotaxis-haptotaxis model with remodeling of non-diffusible attractant
- Analysis of a mixture model of tumor growth
- Sobolev spaces on Riemannian manifolds with bounded geometry: General coordinates and traces
- Numerical simulation of a thermodynamically consistent four-species tumor growth model
- A hybrid ten-species phase-field model of tumor growth
- MATHEMATICAL MODELLING OF CANCER INVASION: THE IMPORTANCE OF CELL–CELL ADHESION AND CELL–MATRIX ADHESION
- A Chemotaxis-Haptotaxis Model: The Roles of Nonlinear Diffusion and Logistic Source
- ON THE COUPLING OF 1D AND 3D DIFFUSION-REACTION EQUATIONS: APPLICATION TO TISSUE PERFUSION PROBLEMS
- GENERAL DIFFUSE-INTERFACE THEORIES AND AN APPROACH TO PREDICTIVE TUMOR GROWTH MODELING
- Mathematical modeling, analysis and numerical approximation of second-order elliptic problems with inclusions
- On a diffuse interface model of tumour growth
- Well-posedness of a Cahn–Hilliard system modelling tumour growth with chemotaxis and active transport
- A multiphase Cahn–Hilliard–Darcy model for tumour growth with necrosis
- Modelling solid tumour growth using the theory of mixtures
- CONVERGENCE OF A CANCER INVASION MODEL TO A LOGISTIC CHEMOTAXIS MODEL
- Local and nonlocal phase-field models of tumor growth and invasion due to ECM degradation
- On the unsteady Darcy–Forchheimer–Brinkman equation in local and nonlocal tumor growth models
- A Hybrid Multiscale Model for Cancer Invasion of the Extracellular Matrix
- Hybrid Models for Simulating Blood Flow in Microvascular Networks
- Analysis and numerical solution of stochastic phase‐field models of tumor growth
- On a structured multiscale model for acid-mediated tumor invasion: The effects of adhesion and proliferation
- MATHEMATICAL MODELLING OF CANCER CELL INVASION OF TISSUE: THE ROLE OF THE UROKINASE PLASMINOGEN ACTIVATION SYSTEM
- Nonlinear partial differential equations with applications
