相場(chǎng)方程N(yùn)eumann問題解的漸近性行為.pdf

1、Y770487援旦大擎碩士學(xué)位論文相場(chǎng)方程N(yùn)eumann問題解的漸近性行為院系：數(shù)學(xué)科學(xué)學(xué)院專業(yè)：基礎(chǔ)數(shù)學(xué)姓名：張振華指導(dǎo)教師：鄭宋穆教授完成日期：2005年4月1日學(xué)校代碼：學(xué)號(hào)t1024602201800復(fù)旦大學(xué)碩士學(xué)位論文iiABSTRACTThephasefieldequationsinquestionwerepl。oposedbyCaginalptodescribethephasetransitionwithfinitethi

2、cknessoftheinterfaceinamaterialWeconsiderinthispapertheasymptoticbehaviorofthephase—fieldequationswithNeumannboundaryconditionsWeprovethatthesolutiontothisproblemwillconvergetoasolutionofanequilibriumproblemastimegoestoi

3、nfinityThemaininstrumentinourproofisaLojasiewiezSimonstyleinequalitywhichisgivenbytwolemmasinChapter2inthispaper。Chapter3isconcernedwiththeproofoftheasymptoticbehaviorSinceweseefromthefirstlemmainChapter2thatourphasefiel

4、dequationproblemisagradientsystem，weonlyhavetoprovethatthereisonlyoneequilibriumpointinthecorrespondingu—limitsetWecallderivetheresultbyusingaLojasiewiczSimoninequalityandasimpliryingmethodproposedbyMAJendoubiKeywordspha