letures notes on nonlinear diffusion equation 尹景学

《letures notes on nonlinear diffusion equation 尹景学》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、LecturesNotesonNonlinearDiusionEquationsbyYinJingxueSeptember,2002Contents1DegenerateParabolicEquations.............................11.1ClassicalDiusionEquations..........................11.2NonlinearDiusionEquations..........................21.3OtherSpecialSolutionsofPorous

2、MediumEquation.............31.4DegenerateParabolicEquations........................31.5DenitionsofGeneralizedSolutions......................42ExistenceofSolutions..................................82.1WeaklyDegenerateEquationswithoutLowerOrderTerms.........82.2WeaklyDegenerateE

3、quationswithLowerOrderTerms...........112.3StronglyDegenerateEquationswithoutTermsofLowerOrder.......172.4GeneralStronglyDegenerateEquations....................193UniquenessofSolutions.................................263.1ComparisonApproach..............................263.2Tes

4、tingTechniques................................293.3Holmgren'sApproach..............................313.4ApproximateHolmgren'sApproach.......................323.5ApproachbyCharacteristicOperators.....................383.6ApproachbytheTheoryofBVSpaces.....................424Finit

5、ePropagationofDisturbances...........................494.1ComparisonApproach..............................494.2ApproachbyMoserIteration..........................534.3ApproachbyEnergyEstimates.........................565FreeBoundaryofSolutions...............................615.1

6、Interfaces.....................................615.2EntropySolutions................................725.3AFreeBoundaryProblem............................786PropertiesofSolutions..................................876.1RegularityofSolutions..............................876.2Locali

7、zationandExtinctionofDisturbances..................926.3AsymptoticBehaviors..............................947AppendixClassesBVandBVx............................98iNonlinearDiusionEquations11DegenerateParabolicEquations1.1ClassicalDiusionEquationsManydiusionprocessescanbedescr

8、ibedbyevolutionarypartialdierentialequations.Inthisse