一类体积填充趋化模型的斑图生成(英文)

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1、应用数学MATHEMATICAAPPLICATA2015。28(1)：115-126PatternFormationinaVolume。-fillingChemotaxisModelGAOHaiyan(i~海燕)，GUOJingjun(郭精军)(SchoolofStatistics，LanzhouUniversityofFinanceandEconomics，Lanzhou730020，Chiha)Abstract：Inthispaper，wedealwiththeNeumanninitial-boundaryvalueprobl

2、eminad—dimen—sionalbox一(O，)(一1，2，3)foravolume-fillingchemotaxissystem／【，，VVU-~U(一u／r、，)’()1=d2V。V+U—V．Nonlineardynamicsnearanunstableconstantequilibriumin(*)isconsidered．Itisprovedthatforanygivengeneralperturbationofmagnitude，linearfastestgrowingmodesdeterminethenonli

3、nearevolutionforthemodel(*)overatimeperiodoftheorderIn8-．Ourresultprovidesarigorousmathematica1descriptionforthepatternformationinthemodel(*)．Keywords：Chemotaxis；Volume—fillingeffect；Patternformation；Nonlineardynam—CLCNumber：O175．26AMS(2000)Su~ectClassification：35K55；

4、92C15；35B35Documentcode：AArticleID：100i-9847(2015)01一O115—121．IntroductionChemotaxisdescribestheactiveorientedmovementofcellsorotherspeciesalongchemi—calgradients．KellerandSegel[]in1970proposedthemathematicalmodelfU一V(DVU—xUVV)，1V一DVV+du一fordescribingtheaggregationpha

5、seofthecellularslimemoldDictyosteliumdiscoideum，whereU(z，￡)，V(z，)denotetheeel1densityandtheconcentrationofchemoattractantre—spectively．Sincethen8vastnumberofresultshavebeendevelopedfortheKeller—Segel—typemodel(formoredetails，seee．g．[2—3]andthereferencestherein)．GUOand

6、HUANGin[4]investigatedthenonlineardynamicsnearanunstableconstantequilibriumoftheclassicalKeller—SegelmodelsatisfyingtheNeumannboundaryconditions*Receiveddate：Feb26，2014Foundationitem：SupportedbytheNationalNaturalScienceFoundationofChina(11361055)，andtheNaturaIScienceF

7、oundationofGansu(145RJZA033)Biography：GAOHaiyan，female，Han，Gansu，associateprofessor，majorinpartialdifferentialequation．MATHEMATICAAPPLICATA2O15onad—dimensionalbox一(0，7【)(：=：1，2，3)．Theirresultsprovedthat1inearfastestgrowingmodesdetermineunstablepatternsforthesystemunde

8、rconsideration．FUeta1．in~51studiedinstabilityintheKeller—Segelmodelwithalogisticsourceandcubicsourcetermrespectively．Theirre