種群細(xì)胞論文具增生擴(kuò)散型種群細(xì)胞中的遷移方程

1、種群細(xì)胞論文：具增生擴(kuò)散型種群細(xì)胞中的遷移方程【中文摘要】本文在Lp(1p<+),研究了一類具年齡結(jié)構(gòu)的增生擴(kuò)散型種群細(xì)胞中具無限周長的遷移方程,討論了這類方程相應(yīng)的遷移算子的譜分析和生成C0半群的性質(zhì),并得到了該遷移算子的譜僅由可數(shù)個具有限代數(shù)重數(shù)的離散本征值組成等結(jié)果。主要結(jié)果如下：1.在Lp(1p<+)空間上,討論該L-R模型所確定的遷移算子AK的生成正C0半群(VK(t)t0,并得到了該正C0半群是不可約的等結(jié)果。2.在Lp(1p<+)空間上,具光滑邊界條件的遷移方程,討論了該L-R模型所確定的遷移算子AK的譜分析,得到了該遷移算子AK的譜由至多可數(shù)個具有限代數(shù)重數(shù)的

2、離散本征值組成,并進(jìn)一步證明了該遷移算子本征值的存在性及該遷移算子的譜在某區(qū)域中僅有限個具有限代數(shù)重數(shù)的離散本征值組成等結(jié)果。3.在Lp(1p<+)空間上,具非光滑邊界條件的遷移方程,討論了該L-R模型所確定的遷移算子AK的譜分析,得到了該遷移算子AK的譜由至多可數(shù)個具有限代數(shù)重數(shù)的離散本征值組成,并進(jìn)一步證明了該遷移算子AK本征值的存在性及該遷移算子AK的譜在某區(qū)域中僅有限個具有限代數(shù)重數(shù)的離散本征值組成等結(jié)果。4.討論該L-R模型相應(yīng)的Cauchy問題的解關(guān)于時間t的漸近穩(wěn)定性及漸近估計等?！居⑽恼縏he objective of this paper is to researc

3、h the transport equations of an age structured proliferating cell population with infinite cycle in Lp(1p<+00) space, It is discussed the spectral analysis of corresponding transport operators for this equation and the properties of the generated Co semigroup; and it is to obtain that the spectru

4、m of the transport operators consists of countable isolate eigenvalues with finite algebraic multiplicities.The main results are showed below:1.It is discussed a mathematical model of L-R in Lp (1p<+) space. obtaining the positivity of the generated Co semigroup(VK(t)t0, and it is to obtain irred

5、ucibility of the generated Co semigroup (VK(t)t0.2. It is discussed the spectral analysis of corresponding transport operator AK for smooth transition operators with infinite cycle in Lp (1p<+) space, and it is to obtain that the spectrum of the transport operators consists of countable isolate e

6、igenvalues with finite algebraic multiplicities.3. It is discussed the spectral analysis of corresponding transport operator AK for partly smooth transition operators with infinite cycle in Lp (1p<+) space, and it is to obtain that the spectrum of the transport operators consists of countable iso

7、late eigenvalues with finite algebraic multiplicities.4. It is discussed a spectral decomposition of solutions of the Cauchy problem. And researched the asymptotically stable and asymptotically estimate about time t.【關(guān)鍵詞】種群細(xì)胞 遷移方程 遷移算子 譜分析 C0半群【英文關(guān)鍵詞】cell population transport equations transport ope

8、rator spectral analysis C0 semigroup【目錄】具增生擴(kuò)散型種群細(xì)胞中的遷移方程摘要3-4ABSTRACT4第1章 緒論7-111.1 研究背景7-81.2 研究進(jìn)展8-91.3 主要結(jié)果9-11第2章 準(zhǔn)備知識11-172.1 空間及范數(shù)11-122.2 算子及性質(zhì)12-17第3章 生成半群的性質(zhì)17-293.1 有關(guān)概念及結(jié)果17-193.2 生成半群19-233.3 生成半群的性質(zhì)23-29第4章 具光滑邊界條件算子A_K的譜分析29-354.1 算子A_K的譜分析29-304.2 算子A_K的本征值30-324.3 A_K的譜的有限性32-35第5章 部分光滑遷移算子A_K的譜分布35-405