一類非線性發(fā)展方程的長期動力學行為.pdf

1、江蘇大學碩士學位論文一類非線性發(fā)展方程的長期動力學行為姓名：張文彬申請學位級別：碩士專業(yè)：應用數(shù)學指導教師：田立新20060612江蘇走學硬士掌位論文ABSTRACTInthispaperintroducingtheconceptofglobalattractortheexistenceofasymptoticsmoothingandtheglobalattractorofaweaklydampedforcedKdVequationon

2、thereallineInthethirdchapter，Theexistenceoftheglobalattractorofaweaklydamped，forcedKorteweg—deVriesequationinthephasespaceL2(R)isprovedAnoptimalasymptoticsmoothingeffectoftheequationisalsoshown，namely，thatforforcesin三2(R

3、)，theglobalattractorinthephasespace三2(R)isactuallyacompactsetinH3陋)Theenergyequationmethodisusedinconjunctionwithasuitablesplittingofthesolutions；thedispersiveregularizationpropertiesoftheequationinthecontextofBourgainsp

4、acesareextensivelyexploited。Inthefo赫chapter，theSobolevinterpolationinequalityandpriorestimateontimetareappliedtoshowtheexistenceofsolutioninunboundeddomain，MoreovegKuratowskii口一noncompactedmeasureareappliedtostudythesmoo