擴(kuò)散方程的條件對(duì)稱及其精確解.pdf

1、Y1091267。0；!‰一攮級(jí)：一～單位代碼：!=!!22學(xué)號(hào)：20042(i～f4!西北大學(xué)碩士學(xué)位論文題目：芝斂友捏的鴦?lì)脉楆偕蹙_鰹作者一盈_塵盤叁指與!教師一雖j量i玨一專業(yè)技術(shù)職務(wù)一熬—i矍一一學(xué)科(專業(yè))一一一座』&一數(shù)堂～～答辯園期學(xué)位授予日期二二OO七年四月Abstract(英文摘要1AblstractThenonlinearphenomenawidelyappearinalmostallthescientificfi

2、eldssuch船physicschemistrybiologysocietyeconomyandSOonWiththedevelopmentofscience，researchesonthenonlinearsystemsaremakingmoreandmoreprogressAsaresultt0dealwiththenonlineaxequationsthatdescribethenonlinearsystemsbecom鶴one

3、ofthemainandhottopicsfortheresearchersItiswellknownthattheconditionalsymmetrymethodisaⅡefficientwayandplayanimportantrolet0studytheexactsolutionofnonlinearpartialdifferentialequation(PDE)ForthenonlinearPDE，therealsohavem

4、anymethodtoohrainexactsolutions，suchastheLiesymmetrydirectmethod，anstizeapproach，geometricmethod，generalizedconditionsymmetryformalvariableseparationapproachandSOOilInthisarticle，weutilizetheconditionalsymmetrymethodtost

5、udynonlineardiffusionequationbasedonphysic8WeobtainsomeinterestingexactsolutiongbyutiuzingconditionalsymmetrymethodtostudynonlinearPDE(135)毗=(D(t1)《kG(t‘)t‘日(讓)Inthechapter1，weintroducesomemethodstostudytheexactsolutiono

6、fnonlinearpartialdifferentialequationsInthechapter2，weutilizetheconditionalsymmetrymethodtostudynonlineardiffusionequation(135)Acompleteclassificationofthefunctionalformsofthereactioncoefficientsandsourcetermsispresented

7、whentheequationadmitstheconditionalsymmetryreductionInthechapter3，wereducePDE(13s)，andobtainsomeexactsolutionsKeywords：symmetrygroup，exactsolution，conditionalsymmetryinvariantSillfacecondition，nonlineardiffusionequationC