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A model describing the growth and the size distribution of multiple metastatic tumors, in "DCDSB", vol. 12, n o 4
"... (Communicated by Christian Schmeiser) Abstract. Cancer is one of the greatest killers in the world, particularly in western countries. A lot of the effort of the medical research is devoted to cancer and mathematical modeling must be considered as an additional tool for the physicians and biologists ..."
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(Communicated by Christian Schmeiser) Abstract. Cancer is one of the greatest killers in the world, particularly in western countries. A lot of the effort of the medical research is devoted to cancer and mathematical modeling must be considered as an additional tool for the physicians and biologists to understand cancer mechanisms and to determine the adapted treatments. Metastases make all the seriousness of cancer. In 2000, Iwata et al. [9] proposed a model which describes the evolution of an untreated metastatic tumors population. We provide here a mathematical analysis of this model which brings us to the determination of a Malthusian rate characterizing the exponential growth of the population. We provide as well a numerical analysis of the PDE given by the model. 1. Introduction. In
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"... c t i v it y e p o r t 2008 Table of contents 1. Team.................................................................................... 1 ..."
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c t i v it y e p o r t 2008 Table of contents 1. Team.................................................................................... 1
Exponential decay for the growthfragmentation/celldivision equation
, 2009
"... We consider the linear growthfragmentation equation arising in the modelling of cell division or polymerisation processes. For constant coefficients, we prove that the dynamics converges to the steady state with an exponential rate. The control on the initial data uses an elaborate L1norm that see ..."
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We consider the linear growthfragmentation equation arising in the modelling of cell division or polymerisation processes. For constant coefficients, we prove that the dynamics converges to the steady state with an exponential rate. The control on the initial data uses an elaborate L1norm that seems to be necessary. It also reflects the main idea of the proof which is to use an antiderivative of the solution. The main technical difficulty is related to the entropy dissipation rate which is too weak to produce a Poincare ́ inequality.