Mathematical and numerical analysis for a model of growing metastatic tumors

DOI10.1016/j.mbs.2008.11.008zbMath1157.92020OpenAlexW1966791626WikidataQ51857600 ScholiaQ51857600MaRDI QIDQ1009602

Federico Verga, Florence Hubert, Assia Benabdallah, Dominique Barbolosi

Publication date: 2 April 2009

Published in: Mathematical Biosciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.mbs.2008.11.008

zbMATH Keywords

asymptotic behavioursemigroup approachcharacteristic schememetastatic tumorsvon Foerster equation

Mathematics Subject Classification ID

Probabilistic models, generic numerical methods in probability and statistics (65C20) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Medical applications (general) (92C50) General theory of partial differential operators (47F05) (C)-semigroups, regularized semigroups (47D60)

Related Items (12)

A mathematical framework for modelling the metastatic spread of cancer ⋮ Approximation by diffusion of renewal equations ⋮ Parameter estimation and treatment optimization in a stochastic model for immunotherapy of cancer ⋮ Mathematical analysis of a two-dimensional population model of metastatic growth including angiogenesis ⋮ A new mathematical model for optimizing the combination between antiangiogenic and cytotoxic drugs in oncology ⋮ Efficient resolution of metastatic tumor growth models by reformulation into integral equations ⋮ Passing to the limit 2D–1D in a model for metastatic growth ⋮ Maximum tolerated dose versus metronomic scheduling in the treatment of metastatic cancers ⋮ Optimisation of Cancer Drug Treatments Using Cell Population Dynamics ⋮ A numerical method for linear Volterra integral equations on infinite intervals and its application to the resolution of metastatic tumor growth models ⋮ Numerical solution of a source identification problem: almost coercivity ⋮ Numerical optimal control of a size-structured PDE model for metastatic cancer treatment

Cites Work

• Unnamed Item
• A model describing the growth and the size distribution of multiple metastatic tumors
• Semigroups of linear operators and applications to partial differential equations
• Transformation semigroups and \(L^ 1\)-approximation for size structured population models
• General relative entropy inequality: an illustration on growth models
• One-Parameter Semigroups for Linear Evolution Equations

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