非線性粘性淺水波方程的整體適定性及極限行為.pdf

1、江蘇大學(xué)碩士學(xué)位論文非線性粘性淺水波方程的整體適定性及極限行為姓名：梁淑娟申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：田立新20081213江蘇大學(xué)碩士畢業(yè)論文InthispapertheglobalwellposednessandlimitbehaviorofthesolutionstothenonlineardispersivewaveequationsarestudiesGettheglobalexistenceanduniquen

2、essofsolutiontothenonlineardispersivewaveequationsforUo∈r(R)Accordingtotheenergyestimate，weresultthelocalwellposednessforUo∈r(R)ThestrongandweaklimitbehaviorofsolutionstothenonlineardispersivewaveequationsaregottenTherea

3、refivesectionsinthispaperThefirstsection，weintroducethebackgroundandactualityandsummarizethemainresultThesecondsection，wewillintroducethebasictheorybasicconceptsneededinthestudy’SThe衄rdsection，weusetheenergyestimateandth

4、eusualextensiontheory，theglobalwell—posednessofthedispersiveDPequationisproved；ThestrongandweaklimitbehaviorofsolutionstothenonlineardispersivewaveequationsaregottenTheforⅡlsection，studiestheweaksolution、entropyweaksolut

5、ionfornonlineardispersivewaveequationsByusingviscousapproximationsandaprioriestimates，weprovetheexistenceofatleastoneweaksolution，satisfyingarestrictedsetofentropyinequalityintheclassr僻)nr@)，andinr(R)r、BV(R)existingentro

6、pyweaksolutionThefifthsection，westudythewell—posednessofthebfamilyequations，wemainlyusedthetheenergyestimateandtheusualextensiontheoryKeywords：Nonlineardispersivewaveequations，DPequation，Well—posedness，Limitbehavior，W色ak