半導(dǎo)體模型中退化漂移---擴(kuò)散問題解的存在性.pdf

1、東南大學(xué)碩士學(xué)位論文半導(dǎo)體模型中退化漂移擴(kuò)散問題解的存在性姓名：楊修引申請學(xué)位級別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：管平2002.1.1半導(dǎo)體模型中退化漂移擴(kuò)敬塑墅堡的查l!絲TheExistenceofSolutiontoADegenerateNonlinearDrift—Di行usionModelforSemiconductorsAbstractInthispaper，westudytheweaksolutionsofthedrift—

2、diffusionmodelforsemiconductoIdeviceTheequationsofthemodelareasfollows裳一V厶=一R(咖)，厶=V巾)一nV妒，(叫)∈QT=n(咿)裳V占=叫哪)△妒=n—P一，，五=一Vr(p)一pV妒，扛，t)∈QTn=nD，P=PD，砂=妒Dn。=P∥=V妒∥=0，n(z，0)=n，，p(x，0)=PI，?！蕁，Vt∈(0，T)扛，t)∈ED(z，t)∈ENz∈Qwherer

3、(0)=r’(O)=0ThemainresultsincludethefollowingtwopartsInthefirstpart，consideringtheinitialandmixedboundaryvalueproblemoftheequationsinthesemiconductorequationswiththeinitialvaluesni，PI∈工霉(n)，weprovetheexistenceofsolutionst

4、othenondegeneratesystembymainlyusingdecouplingmethodandthefixedpointtheoremFirstlywedefinethesolutionmapping：V(元，西∈(工2(Q了1))2toslovethemixedproblemofthePoissonequationI△妒=元一F一，∈L2(Q)，foraet∈(0，T)㈠‰=如Ian。，籌『FN=oThroughthe

5、givenlemma，weobtaintheweaksolution妒∈H1(Q)Whenr’s)￡0(Ys0)constructingtheclosedconvexsetandapplyingAubin’ScompactlemmaandSchauderfixedpointtheorem，weproverespectivelythattheequations釓￡一V(r’(元)V札一禮V幣)r(矗，聲)童n=r(佩，F(xiàn))禮；andPt—