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標題Title: Unboundedness of solutions to a supercritical quasilinear parabolic-parabolic Keller-Segel system in dimension 1 and to a critical one in higher dimensions
作者Authors: Tomasz Cie ́slak
上傳單位Department: 電子工程系
上傳時間Date: 2012-12-8
上傳者Author: 傅俊結
審核單位Department: 電子工程系
審核老師Teacher: 傅俊結
檔案類型Categories: 論文Thesis
關鍵詞Keyword: chemotaxis, infinite-time blowup.
摘要Abstract: Unboundedness of solutions is shown to occur in a one-dimensional quasilinear parabolic- parabolic chemotaxis system for any initial mass. Our result is also independent of the relation between the speeds of the diffusion of cells and chemoattractant. The proof is achieved by contradiction. It uses a virial type inequality together with a boundedness from below of the Liapunov functional associated to the system. Moreover, the same method is applied also in higher dimensions and an unboundedness result is shown in the case of critical quasilinear fully parabolic Keller-Segel system for mass large enough in dimensions n ≥ 3.

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