一類(lèi)反應(yīng)擴(kuò)散方程定態(tài)解的非線性不穩(wěn)定性.pdf

1、華中科技大學(xué)碩士學(xué)位論文一類(lèi)反應(yīng)擴(kuò)散方程定態(tài)解的非線性不穩(wěn)定性姓名：郭延濤申請(qǐng)學(xué)位級(jí)別：碩士專(zhuān)業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：湯燕斌20070529AbstractWiththedevelopingofsciencetechnologycontralmentofthebiologicalfinancialsystemsbringhugeinfluencetotheentiresociety’sdevelopment.Peoplealwaysexp

2、ecttheycanbecontrolledsotheresearchesaboutthestabilityofthesesystemsespeciallyreceivemeattentions.Ifthesystemsarestableweexpectthattheyhavesmallererr.ifthesystemsareinstablewehopetofindthereasonsthenwecanchangetheparamet

3、ertocontrolthemeasily.Weknowthatmanyusefulsystemshavecrespondingmathematicalmodelsfexamplephysicalchemicalbiologicalfinancialsystemscanbedescribedbypartialdifferentialequations.Theequilibriumstateofasystemisastateindepen

4、dentwithtimewhichisoneofthemostimptantstatesitsstabilitydirectlyreflectthestabilityofthewholesystem.Anequilibriumstatecrespondsasteadystatesolutionofanequationsotheresearchesaboutthestabilityofthesteadystatesolutionshave

5、manypracticalsignificances.Chemotaxisisanimptantmodelinbiomedicine.Thisarticlewilldiscussthenonlinearinstabilityofthesteadystatesolutiontothisreactiondiffusionsystem.Itiswellknownthattheperturbationanalysisisaneffectivem

6、ethodtoproofthestabilitysogivenasmallperturbationwediscusstheinfluenceofthesteadystatesolutionfromthissmallperturbation.Fthiswelinearizetheequationswecanfindaparticularsolutiontothelinearizedequationsdiscusstheinstabilit

7、yofthelinearizedequationsfirstly.Thenweusetheenergyestimatetodeterminetheinfluenceofthenonlinearpartoftheequationtothewholesystem.Finallyweusethespectraltheyoflinearoperatenergyestimatetoproofthatlinearinstabilityalwaysi