title: [Autowaves in a model of growth of an invasive tumor].
abstract: A mathematical model for the invasive tumour growth has been constructed, which takes cell division, death, and motility into account. The model includes local cell density and the distribution of nutrient (oxygen) concentration. Cancer cells die in the absence of nutrients; therefore, the distribution of oxygen in tissue substantially affects both the tumour proliferation rate and structure. The model adequately describes the experimentally measured rate of tumour proliferation. The existence of autowave solutions has been demonstrated, and their properties have been investigated. The results are compared with the properties of the Kolmogorov-Petrovskii-Piskunov and Fisher equations. It is shown that the nutrient distribution influences the speed selection and the convergence of the initial conditions to the automodel solution.
authors.forename: A V
authors.initials: AV
authors.lastname: Kolobov
authors.forename: V V
authors.initials: VV
authors.lastname: Gubernov
authors.forename: A A
authors.initials: AA
authors.lastname: Polezhaev
mesh_terms: D000818:Animals; D049109:Cell Proliferation; D006801:Humans; D008954:Models, Biological; D009361:Neoplasm Invasiveness; D009369:Neoplasms / Q000378:metabolism* / Q000473:pathology / Q000503:physiopathology