二維橢圓—拋物趨化性模型解的范數(shù)性質(zhì).pdf

1、華中科技大學(xué)碩士學(xué)位論文二維橢圓—拋物趨化性模型解的范數(shù)性質(zhì)姓名：孫貴玲申請學(xué)位級別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：楊茵20070529AbstractMathematicalBiologymainlyaimsatecologicalsystemonespecificpropertyofecologicalsystemisthatthebodyinthatcancatchtheexternalstimulateresponsetothat

2、thispropertycanbecalledTaxis.Asweknowntherearemanydifferenttypesoftaxissuchas:aerotaxischemotaxisgeotaxishaptotaxissoon.Thispapermainlyintroducechemotaxiswhichiswidelyinterestedbymanymathematicalsbiologists.Thechemotaxis

3、movementisthebodymovetowardsthechemicalswhiegoodfthemawayfromthechemicalswhicharebadfthem.Infactitisnotonlyinanimalinsectecologythatchemotaxisisimptantitcanbeequallycrucialinbiologicalprocesswheretherearenumerousexamples

4、.Fexamplewhenabacterialinfectioninvadesthebodyitmaybeattackedbymovementofcellstowardsthesourcseasaresultofchemotaxis.Convincingevidencesuggeststhatleukocytecellsinthebloodmetowardsaregionofbacterialinflammationtocounteri

5、tbymovingupachemicalgradientcausedbytheinfection.Sowecansaythatchemotaxismodelhascloserelativewithmedicinestudyofthemodelhasgreatactivemeaninginthemedicine.Awidelystudiedchemotacticphenomenonisthatexhibitedbytheslimemold

6、DictyosteliumDiscoideumwheresinglecellamoebaemetowardsregionsofrelativelyhighconcentrationsofachemicalcalledcyclicAMPwhichisproducedbytheamoebaethemselves.Sofarmanypapershavedeeplystudiedthismodelundersomespecialcondatio

7、nsthereisacriticalnumberπ?αχwhen??u0(x)dxπ?αχthesolutionwillblowupinfinitetime.Thepapermainlyconsiderthecaseofε=0reactiontermαu?βvthemodelisshowedin(1.3).ThispapermainlystudiedtherelativepropertyoftheK?Smodel:thelocalexi

8、stenceglobalexistenceregulitytheblowuppropertytomodel(1.3).Firstthepaperdiscussthelocalexistenceofsolutionstotheequivalentfmofmodel(1.3)byuseoftherelativepropertyofanalyticsemigroupsectialoperatthendiscusstheregularityof

9、solutions.Meanwhilewegetthenonnegativepropertyofuv.Inthelattersectionthecaseofaα≥bβwerestudiedbyuseoftwodermomenttheestimateoftwodermomentsoweconcludethatalthoughreactiontermseffectK?Smodelbyadegreebutthecriticalnumberof