Well-posedness for a class of phase-field systems modeling prostate cancer growth with fractional operators and general nonlinearities
DOI10.4171/RLM/969zbMath1493.35123arXiv2104.00444OpenAlexW3141784742WikidataQ114021390 ScholiaQ114021390MaRDI QIDQ2154800
Pierluigi Colli, Gianni Gilardi, Juergen Sprekels
Publication date: 15 July 2022
Published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2104.00444
PDEs in connection with biology, chemistry and other natural sciences (35Q92) Fractional partial differential equations (35R11) Initial-boundary value problems for second-order parabolic systems (35K51)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- On a Cahn-Hilliard type phase field system related to tumor growth
- On a hyperbolic Keller-Segel system with degenerate nonlinear fractional diffusion
- Global solutions for a hyperbolic-parabolic system of chemotaxis
- An adaptive multigrid algorithm for simulating solid tumor growth using mixture models
- Numerical solutions for fractional reaction-diffusion equations
- 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
- Three-dimensional multispecies nonlinear tumor growth. II: Tumor invasion and angiogenesis
- Analysis of a Cahn-Hilliard-Brinkman model for tumour growth with chemotaxis
- Three-dimensional multispecies nonlinear tumor growth. I: Model and numerical method
- Deep quench approximation and optimal control of general Cahn-Hilliard systems with fractional operators and double obstacle potentials
- Long-time dynamics and optimal control of a diffuse interface model for tumor growth
- 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
- On a phase field model of Cahn-Hilliard type for tumour growth with mechanical effects
- 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
- Sulle equazioni differenziali astratte lineari del primo e del secondo ordine negli spazi di Hilbert
- Soluzioni ordinarie e genralizzate del problema di Cauchy per equazioni differenziali astratte lineari del secondo ordine in spazi di Hilbert
- Analysis of a mixture model of tumor growth
- Numerical simulation of a thermodynamically consistent four-species tumor growth model
- A hybrid ten-species phase-field model of tumor growth
- 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
- A class of time‐fractional reaction‐diffusion equation with nonlocal boundary condition
- On a diffuse interface model of tumour growth
- Fractional Diffusion Equations and Anomalous Diffusion
- Space-time fractional diffusion in cell movement models with delay
- Mathematical modelling of tumour growth and treatment
- Well-posedness and regularity for a fractional tumor growth model
- Mathematical analysis and simulation study of a phase-field model of prostate cancer growth with chemotherapy and antiangiogenic therapy effects
- Asymptotic analysis of a tumor growth model with fractional operators
- Optimal control of cytotoxic and antiangiogenic therapies on prostate cancer growth
- Well-posedness, regularity and asymptotic analyses for a fractional phase field system
- Analysis of a diffuse interface model of multispecies tumor growth
- Optimal distributed control of a diffuse interface model of tumor growth
- MATHEMATICAL ANALYSIS AND CHALLENGES ARISING FROM MODELS OF TUMOR GROWTH
- Nonlinear Differential Equations of Monotone Types in Banach Spaces
This page was built for publication: Well-posedness for a class of phase-field systems modeling prostate cancer growth with fractional operators and general nonlinearities