一類二元合金等溫固化模型平衡態(tài)的混合邊值問題.pdf

1、東南大學(xué)碩士學(xué)位論文一類二元合金等溫固化模型平衡態(tài)的混合邊值問題姓名：張益申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：管平20060301AbstractAbstract：Inthispaperwestudythemixed—boundaryvalueproblemintheequilibriumstateofaphasefieldmodelfortheisothermalsolidificationprocessofabinarya11

2、0弘Theequationsoftheproblemread：l一￡2△≯=Fl(糾c而(毋)inndiv(D1(≯)Ve)=div(D2(c，妒)V咖)innI≯=如，c；匈onrD；器=器=0onrN(11)(12)(13)Theparametereaccountsfortherelativedensityoftheadloytheparameter妒accotmtsforthesolidificationstateoftheall

3、oyandisequalto0inthesolidphaseandequals1intheliqmdphaseWeinvestigatethenondegeneratecaseoftheproblem，provetheexistenceofthesolutionunderaL∞estimate，andgiveamaximalprincipaltotheproblemThispaperisorganizedinthefollowingwa

4、y：Insection1wemakearegularizationoftheproblembyacutoffmethodfirstandprovetheexistenceofthesolutionoftheregldari=zedproblemwiththefixedpointtheorem，thenweprovethesolutionoftheregularizedproblemisMsosolutionoftheorigialpro

5、blemafteranestimateInsection2weprovetheuniquenessofthesolutionforthenondegeneratecaseoftheproblemFinallyinsection3weestablishamaximumprincipleunderextraassumptionsonthenonlineartermsKeywords：Mixedbotmdaryproblem；Nondegen