Search results for " 92C17"

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Modeling multiple taxis: Tumor invasion with phenotypic heterogeneity, haptotaxis, and unilateral interspecies repellence

2021

We provide a short review of existing models with multiple taxis performed by (at least) one species and consider a new mathematical model for tumor invasion featuring two mutually exclusive cell phenotypes (migrating and proliferating). The migrating cells perform nonlinear diffusion and two types of taxis in response to non-diffusing cues: away from proliferating cells and up the gradient of surrounding tissue. Transitions between the two cell subpopulations are influenced by subcellular (receptor binding) dynamics, thus conferring the setting a multiscale character. We prove global existence of weak solutions to a simplified model version and perform numerical simulations for the full se…

Tumor invasionTaxisComputational biologyBiologyMutually exclusive events01 natural sciencesHaptotaxisMultiple taxis and review of modelsRC0254Mathematics - Analysis of PDEsSDG 3 - Good Health and Well-beingCell Behavior (q-bio.CB)Numerical simulationsFOS: MathematicsDiscrete Mathematics and CombinatoricsNonlinear diffusionQA Mathematics0101 mathematicsGlobal existenceQARC0254 Neoplasms. Tumors. Oncology (including Cancer)Genetic heterogeneityInterspecies repellenceApplied Mathematics010102 general mathematicsI-PWCell subpopulationsPhenotypeAC010101 applied mathematicsFOS: Biological sciencesQuantitative Biology - Cell Behavior35Q92 (Primary) 92C17 92C50 (Secondary)Analysis of PDEs (math.AP)Discrete & Continuous Dynamical Systems - B
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Existence and uniqueness of global classical solutions to a two species cancer invasion haptotaxis model

2017

We consider a haptotaxis cancer invasion model that includes two families of cancer cells. Both families, migrate on the extracellular matrix and proliferate. Moreover the model describes an epithelial-to-mesenchymal-like transition between the two families, as well as a degradation and a self-reconstruction process of the extracellular matrix. We prove positivity and conditional global existence and uniqueness of the classical solutions of the problem for large initial data.

Mathematics - Analysis of PDEs35A01 35B65 35Q92 92C17FOS: MathematicsAnalysis of PDEs (math.AP)
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