本文選題：腫瘤生長　切入點(diǎn)：偏微分方程　出處：《廣東工業(yè)大學(xué)》2012年碩士論文　論文類型：學(xué)位論文

【摘要】：本文研究了兩個(gè)腫瘤生長的偏微分方程模型,嚴(yán)格分析了其解整體解的適定性.全文共分三章. 第一章是緒論,分別介紹了腫瘤生長模型的歷史背景和發(fā)展?fàn)顩r. 第二章研究了一個(gè)腫瘤化學(xué)治療反應(yīng)的空間結(jié)構(gòu)的數(shù)學(xué)模型,這是一個(gè)動力系統(tǒng)模型,它是偏微分方程的自由邊界問題.假設(shè)腫瘤的繁殖和死亡由局部藥物濃度決定.在一些條件下,通過運(yùn)用拋物方程的Lp理論、Banach不動點(diǎn)定理證明了這個(gè)問題局部解的存在唯一性,然后用延拓方法得到了整體解的存在唯一性.在另外一些條件下,通過運(yùn)用反應(yīng)擴(kuò)散方程的上、下解方法,得到了：當(dāng)0w≤w*時(shí),此模型沒有穩(wěn)態(tài)解；當(dāng)w*ww時(shí),此模型有唯一的穩(wěn)態(tài)解(ws,Rs). 第三章研究了一個(gè)大腦膠質(zhì)瘤細(xì)胞生長情況的模型,這是一個(gè)交叉擴(kuò)散模型.它包含基質(zhì)金屬蛋白酶和營養(yǎng)物濃度,并且考慮了由趨藥性、趨觸性和趨附性產(chǎn)生的效應(yīng).這個(gè)模型耦合了三個(gè)半線性拋物方程和一個(gè)常微分方程.通過運(yùn)用Banach不動點(diǎn)定理、拋物方程的Schauder估計(jì)及拋物方程的Lp估計(jì)證明了這個(gè)問題局部解的存在唯一性,然后利用延拓方法得到了整體解的存在唯一性.
[Abstract]:In this paper, two partial differential equation models for tumor growth are studied, and the suitability of the global solution is strictly analyzed. There are three chapters in this paper. The first chapter introduces the historical background and development of tumor growth model. In the second chapter, we study a mathematical model of the spatial structure of tumor chemotherapeutic response, which is a dynamic system model. It is a free boundary problem for partial differential equations. It is assumed that the propagation and death of tumors are determined by local drug concentration. Under some conditions, the existence and uniqueness of the local solution of the problem are proved by using the Banach fixed point theorem of the parabolic equation. Then the existence and uniqueness of the global solution are obtained by using the continuation method. Under some other conditions, by using the method of upper and lower solutions of the reaction diffusion equation, it is obtained that the model does not have a steady solution when 0 w 鈮，

本文編號：1561706