本文印刷
全画面プリント
GCOEセミナー
過去の記録 ～04/22｜次回の予定｜今後の予定 04/23～
2009年09月08日(火)
16:15-17:15 数理科学研究科棟(駒場) 123号室
Glenn Webb 氏 (Vanderbilt University)
Analysis of a Model for Transfer Phenomena in Biological Populations (ENGLISH)
Glenn Webb 氏 (Vanderbilt University)
Analysis of a Model for Transfer Phenomena in Biological Populations (ENGLISH)
[ 講演概要 ]
We study the problem of transfer in a population structured by a continuum variable corresponding to the quantity being transferred. The transfer of the quantity occurs between individuals according to specified rules. The model is of Boltzmann type with kernel corresponding to the transfer process. We prove that the transfer process preserves total mass of the transferred quantity and the solutions of the simple model converge weakly to Radon measures. We generalize the model by introducing proliferation of individuals and production and diffusion of the transferable quantity. It is shown that the generalized model admits a globally asymptotically stable steady state, provided that transfer is sufficiently small. We discuss an application of our model to cancer cell populations, in which individual cells exchange the surface protein P-glycoprotein, an important factor in acquired multidrug resistance against cancer chemotherapy.
We study the problem of transfer in a population structured by a continuum variable corresponding to the quantity being transferred. The transfer of the quantity occurs between individuals according to specified rules. The model is of Boltzmann type with kernel corresponding to the transfer process. We prove that the transfer process preserves total mass of the transferred quantity and the solutions of the simple model converge weakly to Radon measures. We generalize the model by introducing proliferation of individuals and production and diffusion of the transferable quantity. It is shown that the generalized model admits a globally asymptotically stable steady state, provided that transfer is sufficiently small. We discuss an application of our model to cancer cell populations, in which individual cells exchange the surface protein P-glycoprotein, an important factor in acquired multidrug resistance against cancer chemotherapy.
