關(guān)于半導(dǎo)體粘性量子流體動(dòng)力學(xué)模型的數(shù)學(xué)分析.pdf

1、東北師范大學(xué)碩士學(xué)位論文關(guān)于半導(dǎo)體粘性量子流體動(dòng)力學(xué)模型的數(shù)學(xué)分析姓名：黃雪申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：張凱軍20050501AbstractTheviscousquantumhydrodynamicmodelarisesfromphysicsIthashigervahienotonlyintheresearchfieldsbutalsoinpractice，therefme，ithasbeenaveiyL『jI[)olI

2、aIttpartinsemiconductorfieldTheviscousquantumhydrodynamicnlodelis(；olnpos(。(IoItwoconservationequationswithparticledensityn，thecurrentdensity。TandthePoissonequationTwoconservationequationsarederivedfromaWigner—FokkerPlan

3、ckmodel：theycontainathird—orderquantumcorrectiontermandsecond—orderviscollstermOurobjectinthispaperisthesteady—statevisousquantumhy&odynamicmodelinonespacedimensionwestudymainlyexistenceanduniquenessofsolut，ionsiIjthephy

4、sicallymotivatedtheDirichletandNeumannboundaryconditions，twoinlpoItanllimitsaswellFirstofa11inthispaperwereformulatetheproblema8afourth—orderellipticequationbyusinganexponentialvariabletransformationSecond，webuildupapIio

5、：‘iestimatesofsolutionsbyusingthetruncatedmethodinthecaseof”weakly”subsonicAndthen，wegetexistenceofsolutionswhichisbasedOnapriOI’iestimagestothefourth—orderequationbytheLeraySchauderfixedpointtheoremInthetbllowingweptove

6、theuniquenessofsolutionwhenthephysicalparameterisenoughsmall【Iltheend，weproveinviscidlimitandzero—spacechargelimitKeywords：Viscousquantumhydrodynamicmodel，existenceanduniqtlenessotsolutions，inviscidlimit，zero—space—charg