Boltzmann方程的Tjon-Wu模型.pdf

1、華中科技大學(xué)碩士學(xué)位論文Boltzmann方程的TjonWu模型姓名：楊曉俠申請學(xué)位級別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：張顯文20061022AbstractBoltzmannequationisthepracticallymathematicalmodeltodescribethetimespaceevolutionatastatisticallevelofthepositionvelocitydistributionfunctiono

2、fparticlesinadilutegas.Howeverinviewofthecomplicationofthecollisionoperatthestudyoftheequationisverydifficult.Tjon?Wuequation([1]?[4])Tjon?WumodeloftheBoltzmannequationwitheasierfmwasderivedfromthespatiallyhomogeneousBol

3、tzmannequationbyuseoftheAbeltransfmation.Severalauthsinvestigatedtheequation(seee.g.:[5]?[11]).ThispaperstudiesageneralizedTjon?WuequationproposedbyA.Lasola[11].FirsttheCauchyproblemftheequationisconsidered.1.Weobtainthe

4、existenceuniquenessfthesolutionoftheCauchyproblembymeansofsemigroupthey.2.WeshowpositivityestimatesofmomentsofseniderfthesolutionoftheCauchyprobleminsomespecialconditionsbyusingthepropertiesoffixedpointthebasicmomentineq

5、ualitythemethodofsuccessiveapproximations.Secondwediscussthestationaryproblemftheequation.1.WeestablishtheexistenceofthestationarysolutionthroughverifyingtheconditionoftheSchauderfixedpointtheem.2.Weshowthatthestationary

6、solutionispositivebymeansofpositivityoftheoperatPthepropertiesoffixedpoint.3.Weobtaintheuniquenesstheasymptoticstabilityofthestationarysolution(A.Lasola[11]hasprovedthatthestationarysolutionftheequationisexponentiallysta

7、bleinweaktopology).Thepositivityofthestationarysolutionplaysanimptantroleintheproofofstability.ItallowsustoapplytheKantovich?Rubinsteinmaximumprincipletoprovethatthestationarysolutionisgloballyasymptoticallystableinstron