Asymptotic analysis of a tumor growth model with fractional operators
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Publication:5151333
DOI10.3233/ASY-191578zbMath1476.35284arXiv1908.10651OpenAlexW2979453440MaRDI QIDQ5151333
Pierluigi Colli, Gianni Gilardi, Juergen Sprekels
Publication date: 17 February 2021
Published in: Asymptotic Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1908.10651
well-posednessasymptotic analysisfractional operatorsregularity of solutionstumor growth modelsCahn-Hilliard systems
Smoothness and regularity of solutions to PDEs (35B65) Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Fractional derivatives and integrals (26A33) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Cell biology (92C37) Cell movement (chemotaxis, etc.) (92C17) Fractional partial differential equations (35R11) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)
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Cites Work
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- On a Cahn-Hilliard type phase field system related to tumor growth
- On a hyperbolic Keller-Segel system with degenerate nonlinear fractional diffusion
- Asymptotic analyses and error estimates for a Cahn-Hilliard type phase field system modelling tumor growth
- Is a nonlocal diffusion strategy convenient for biological populations in competition?
- Global solutions for a hyperbolic-parabolic system of chemotaxis
- Analysis of a Cahn-Hilliard system with non-zero Dirichlet conditions modeling tumor growth with chemotaxis
- An adaptive multigrid algorithm for simulating solid tumor growth using mixture models
- Erratum to: ``On the nonlocal Cahn-Hilliard-Brinkman and Cahn-Hilliard-Hele-Shaw systems
- On the Cahn-Hilliard-Brinkman system
- Vanishing viscosities and error estimate for a Cahn-Hilliard type phase field system related to tumor growth
- Numerical solutions for fractional reaction-diffusion equations
- Compact sets in the space \(L^ p(0,T;B)\)
- Optimal control of treatment time in a diffuse interface model of tumor growth
- Hybrid time-space dynamical systems of growth bacteria with applications in segmentation
- On a diffuse interface model for tumour growth with non-local interactions and degenerate mobilities
- On a Cahn-Hilliard-Darcy system for tumour growth with solution dependent source terms
- Three-dimensional multispecies nonlinear tumor growth. II: Tumor invasion and angiogenesis
- Analysis of a Cahn-Hilliard-Brinkman model for tumour growth with chemotaxis
- The Cahn-Hilliard-Hele-Shaw system with singular potential
- Three-dimensional multispecies nonlinear tumor growth. I: Model and numerical method
- On a multi-species Cahn-Hilliard-Darcy tumor growth model with singular potentials
- Optimal distributed control of a Cahn-Hilliard-Darcy system with mass sources
- Long-time dynamics and optimal control of a diffuse interface model for tumor growth
- Optimal treatment for a phase field system of Cahn-Hilliard type modeling tumor growth by asymptotic scheme
- Optimal distributed control of an extended model of tumor growth with logarithmic potential
- Optimal distributed control of a generalized fractional Cahn-Hilliard system
- Mesh free alternate directional implicit method based three dimensional super-diffusive model for benign brain tumor segmentation
- Well-posedness for the Brinkman-Cahn-Hilliard system with unmatched viscosities
- Optimality conditions for an extended tumor growth model with double obstacle potential via deep quench approach
- Global weak solutions and asymptotic limits of a Cahn-Hilliard-Darcy system modelling tumour growth
- Well-posedness and regularity for a generalized fractional Cahn-Hilliard system
- 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
- On the long time behavior of a tumor growth model
- Sliding mode control for a phase field system related to tumor growth
- Bayesian calibration, validation, and uncertainty quantification of diffuse interface models of tumor growth
- Well-posedness of the Hele-Shaw-Cahn-Hilliard system
- A Cahn–Hilliard–Darcy model for tumour growth with chemotaxis and active transport
- Analysis of a mixture model of tumor growth
- Numerical simulation of a thermodynamically consistent four-species tumor growth model
- Analysis of a Darcy--Cahn--Hilliard Diffuse Interface Model for the Hele-Shaw Flow and Its Fully Discrete Finite Element Approximation
- Numerical analysis of fractional-order tumor model
- ON THE FOUNDATIONS OF CANCER MODELLING: SELECTED TOPICS, SPECULATIONS, AND PERSPECTIVES
- GENERAL DIFFUSE-INTERFACE THEORIES AND AN APPROACH TO PREDICTIVE TUMOR GROWTH MODELING
- Optimal control for a nonlinear mathematical model of tumor under immune suppression: A numerical approach
- On a diffuse interface model of tumour growth
- Well-posedness of a Cahn–Hilliard system modelling tumour growth with chemotaxis and active transport
- Fractional Diffusion Equations and Anomalous Diffusion
- A multiphase Cahn–Hilliard–Darcy model for tumour growth with necrosis
- Fractionally delineate the neuroprotective function of calbindin-D28k in Parkinson’s disease
- Space-time fractional diffusion in cell movement models with delay
- Mathematical modelling of tumour growth and treatment
- Well-posedness, regularity and asymptotic analyses for a fractional phase field system
- Free Energy of a Nonuniform System. I. Interfacial Free Energy
- Analysis of a diffuse interface model of multispecies tumor growth
- Optimal distributed control of a diffuse interface model of tumor growth
- The nonlocal Cahn–Hilliard–Hele–Shaw system with logarithmic potential
- MATHEMATICAL ANALYSIS AND CHALLENGES ARISING FROM MODELS OF TUMOR GROWTH
