兩類反應(yīng)擴(kuò)散方程組解的性質(zhì)的研究.pdf

1、南京信息工程大學(xué)碩士學(xué)位論文兩類反應(yīng)擴(kuò)散方程組解的性質(zhì)的研究姓名：鄒贏申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：李剛20050501AbstractAbstractThisdissertationisdevotedtotheglobalexistenceanduniquenessofsolutionstotheinitialandboundaryvalueproblemforaclassofdegeneratereactiondifus

2、ionsystemandtheuniformboundednessofsolutionstosystemsinathreespeciesmodelwithcrossdifusions.Thedissertationcontainsthreeparts:InChapter1thebasicbackgroundadvancedstudiesandthemainideaofthisdissertationisintroduced.InChap

3、ter2weconsideraclassofdegeneratereactiondifusionsystem:uie=er(u)If(xtu)(xt)EOx(0，二)，i=12，二，(0.1)theglobalexistenceandofsolutionstotheinitialandboundaryvalueproblemarediscussed.HereQisaLipschitzboundeddomaininR0withasmoot

4、hboundary8S2，vistheunitoutwardnormaltoM.n21andvectorfunctionx=(xx...x).Byintroducingtruncatedfunctionweapplycompacttheorytoobtaintheglobalexistenceanduniquenessofsolutionstotheinitialandboundaryvalueproblemwhereweassumet

5、hatthenonnegativeinitialvaluesu(x0)=.1(.)eL(0)i.e.ina“l(fā)ower“functionalspacethenonlineardifusiontermrj()andthereactiontermf(xtu)satisfysomeassumptionstooInChapter3weconsidertheuniformboundednessofsolutionstosystemsinathre

6、ecompetitionspeciesmodelwithcrossdifusions:司司勸(0，(0，(0，任任任、日J(rèn)、月了八勺(x，(x，(x，(al(a=腸，aua3s)uL心，722Va23s)VIP3su(a，一b3u一C3V一b。一。t，一ds)u一62。一。2，一d2s)V么S)S[0小[01]x[01]x(0.2)全魚=paVaVu(x0)=ua(x)20V(x0)=VO(x)_Os(x0)=so(x)0X二二x任oi