Boltzmann方程的穩(wěn)定性及一維情形下解的多項(xiàng)式衰減性.pdf

1、華中科技大學(xué)碩士學(xué)位論文Boltzmann方程的穩(wěn)定性及一維情形下解的多項(xiàng)式衰減性姓名：楊云飛申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：張顯文20060630AbstractBoltzmannequationisanintegrodifferentialequationsatisfyingprobabilitydensity.Theprobabilitydensityisprobabilitywhichdescribethepossib

2、ilitythatamoleculeinthegasappeararoundsomestate.Theequationprovidesamathematicalmodelfthestatisticalevolutionofthemoderatelyrarefiedgas.Itappearsinavarietyofscienceshaslotsofapplicationsinastrophysicsaerospaceengineering

3、nuclearengineering.ThestabilitytheyofBoltzmannequationisofhightheeticalvalue.NowwehaveconcludedthestabilitytheyofhardspheremodelonedimensionalBoltzmannequationwithinelasticcollitions.Inthehardspheremodelwheninitialdatame

4、etsexponentiallydecayinglocalexistencepositivityofmildsolutionswasstudiedbyGlikson[1]KanielShinbrot[2]faunboundeddomainaboundeddomainparativelyspeakingthere’slessstudyofL1stabilityofthesolutionofBoltzmannequation.Underth

5、ehomogeneousspaceconditionArkeryd[4]provestheL1stabilityofLyapunovclass.UndertheinhomogeneousspaceconditionSeungYealHa[5]concludestheestimationofL1stabilityofthemildsolutionunderMaxwellmoleculemodelinBoltzmannequationSeu

6、ngYealHa[67]basedonthe[891011]byToscaniothershasestablishedtheL1stabilityaboutthesmallinitialdataftheclassicalsolutionofexponentiallypolynomiallydacaying.Theliterature[12]hasappliedthisconclusiontothemildsolutionofexpone

7、ntiallydecaying.InonedimensionalBoltzmannequationwithinelasticcollisionSeungYealHa[13]presentstheL1stabiltyofthemildsolution.MywkliesmainlywiththeproofofL1stabilityofthepolynomialdacayingweaksolutionsoftheBoltzmannequati

8、onthepolynomialdacayingpropertyofthesolutionsunderonedimensionalBoltzmannequationwithinelasticcollision.Withthemethodfrom[6712]wehaveaccdinglyprovedtheconclusionofL1stabilitytopartsoftpotentialsallhardpotentials.SeungYea

9、lHapresentstheboundednessoftheclassicalsolutiontheL1stabilityofonedimensionalBoltzmannequationwithinelasticcollitionswhileIhaveprovedthepolynomialdecayingpropertyofthemildsolutionsbymeansofthebasicpropertiesofcollisionop