高維單守恒律方程的非自相似基本波及其相互作用.pdf

1、密級(jí)：公開高維單守恒律方程的非自相似基本波及其相互作用NonselfsimilarElementaryWavesoftheMultidimensionalScalarConservationLawTheirInteractions(申請(qǐng)汕頭大學(xué)理學(xué)碩士學(xué)位論文）院(系、所)：理學(xué)院數(shù)學(xué)系專業(yè)：應(yīng)用數(shù)學(xué)研究生：牛海萍指導(dǎo)教師：楊小舟副教授o年五月AbstractInthisthesiswegetthenonselfsimilareleme

2、ntarywavesformultidimensionalScalarconservationequationandtheirglobalanalyticsolutioninanotherkindofapproachwhichisdifferentfromusualselfsimilartransformation.Thesolutionhasnewstructureforanyfixedtimet.Thisthesisisdivide

3、dintothreeparts.Inthefirstpartofthethesiswediscusselementarywavesandtheirinteractionsfortwodimensionalequation.Inthiscasewelettheinitialdiscontinuitydividetheinitialplaneintotwoinfiniteparts.Wegettheglobalanalyticsolutio

4、nspecificallywheretheinitialdiscontinuityisparabolafortwodimensionalequation.Inthesecondpartofthethesisweconsideranotherspecialkindoftwodimensionalequation’selementarywavesandtheirinteractions.Inthiscasetheinitialdiscont

5、inuitydividetheinitialplaneintoaninfiniteregionandafiniteclosedregion.Itisexplicitthatthedistributionofthesolutioninthiscaseisdifferentfromtheformerinessence.Westudythecasethattheinitialdiscontinuityisaunitcircleandaconc

6、aveclosedcurveseparatelyfortwodimensionalequationandwefindthattheglobalsolutionoftwodimensionalScalarconservationequationcanvaryfreely.Inthelastpartofthethesiswestudyelementarywavesandtheirinteractionsforathreedimensiona

7、lequation.Herethedistributionisaunitsphereandwegetthethreedimensionalsolutionforthethreedimensionalequationwhilewecannotgetitinusualselfsimilarmathod.Theresultwegetisoneoftheleastachievementsfornonsymmetrictypeinthreedim