一類Kirchhoff型波動方程組的整體適定性.pdf

1、哈爾濱工程大學(xué)碩士學(xué)位論文一類Kirchhoff型波動方程組的整體適定性姓名：姜曉麗申請學(xué)位級別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：楊海歐20120311哈爾濱工程大學(xué)碩士學(xué)位論文AbstractThisworkcarriesoutqualitativestudiesonhyperbolicequationsofKirchhofftypewithdampingandnonlinearsourcetermsinaboundeddomainWes

2、tudytheinitialboundaryvalueproblemconcerningthissystemCharacterizationswithrespecttOqualitativepropertiesofthesolutioninaboundeddomainQunderthreeenergylevelsofE(o)：globalexistence，blow—up，asymptoticbehaviorInparticular，i

3、nfinitetimeblowupresultwitharbitraryhighinitialenergyz(o)0isgiveninthisarticleThisworkisbasedonpotentialwellstheory，concavitymethodandcombiningwiththeenergymethodApplyingthesetheoriesandmethods，wearemoremeticulousdemonst

4、ratesthestructureandpropertiesofsolutionsofthewaveequationswithKirchhofftypein嘲(Q)spaceItisdesignedtohaveatheoryinstructionfunctionforthesameprobleminphysicsandengineeringmodelConsequently，thisworkfurtherenrichesanddevel

5、opspotentialwelltheoryFirstly，thispaperestablishesthevariationaltheorycorrespondingtheKirchhoff’Stypewaveequations，anddefinestheequalityofenergyconservationandalsosomerelatedfunction—alsThentherelevantpropertiesofthefami

6、lyofpotentialwellsandinvariantsetsaregivenunderpositiveenergyandnon—positiveenergyCombiningwithGalerkinmethodandenergyestimatemethod，wegettheoptimumconditionfortheglobalexistenceoftheweaksolutionscorrespondingtheabovesys

7、temandthenwediscussalongtimebehaviorofthesolutionsMoreoverundersomehypotheticalconditions，theglobalexistenceisyieldedatcriticalenergylevelFurther，thispaperstudiesglobalnonexistenceforsuchKirchhoff’Stypeequationsinthreein

8、itialenergylevelsUndertheappropriateassumptions，westudythefinitetimeblowupresultsbythepotentialwellmethodandconvexmethodforthecorrespondingproblemInsummary，thetheoreticalsignificanceofthispaperisreflectedinthefollowingin

9、nova—tionpoints：Firstly，inthecurrentmanyapplicationsandresearcheswithpotentialwelltheoryhavefocusedontheequationswithweakdampingterms，Butthispotentialwellsmethodwillbeappliedinnonlinearwaveequationswithweaklydampedterms，

10、employingitwesolvetheglobalposed—nessofKirchhoff—typewaveequationsSecondly，asfarasweknow，thestudyofKirchhofftypewaveequationsatlowinitialenergyarenotinvolvedwiththeasymptoticbehav—ior，inthispaperweareinterestedindiscussi