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1、TranslationsofMATHEMATICALMONOGRAPHSVolume140TravelingWaveSolutionsofParabolicSystemsAizikI.VolpertVitalyA.VolpertVladimirA.VolpertATHEMATICMALNTRHTOSMHEISITWSAOICCIAmericanMathematicalSocietyREEAGEWMETYMProvidence,RhodeIslandAF8O8UNDED18A.I.Volpert,Vit.A.Vol
2、pert,Vl.A.VolpertBEGUWIEVOLNY,OPISYVAEMYEPARABOLIQESKIMISISTEMAMITranslatedbyJamesF.HeydafromanoriginalRussianmanuscript2000MathematicsSubjectClassification.Primary35K55,80A30;Secondary92E10,80A25.Abstract.Travelingwavesolutionsofparabolicsystemsdescribeawide
3、classofphenomenaincombustionphysics,chemicalkinetics,biology,andothernaturalsciences.Thebookisdevotedtothegeneralmathematicaltheoryofsuchsolutions.Theauthorsdescribeindetailsuchquestionsasexistenceandstabilityofsolutions,propertiesofthespectrum,bifurcationsofs
4、olutions,approachofsolutionsoftheCauchyproblemtowavesandsystemsofwaves.Thefinalpartofthebookisdevotedtoapplicationstocombustiontheoryandchemicalkinetics.Thebookcanbeusedbygraduatestudentsandresearchersspecializinginnonlineardifferentialequations,aswellasbyspecia
5、listsinotherareas(engineering,chemicalphysics,biology),wherethetheoryofwavesolutionsofparabolicsystemscanbeapplied.LibraryofCongressCataloging-in-PublicationDataVolpert,A.I.(A˘ızikIsaakovich)[Begushchievolny,opisyvaemyeparabolicheskimisistemami.English]Travel
6、ingwavesolutionsofparabolicsystems/AizikI.Volpert,VitalyA.Volpert,VladimirA.Volpert.p.cm.—(Translationsofmathematicalmonographs,ISSN0065-9282;v.140)Includesbibliographicalreferences.ISBN0-8218-4609-4(acid-free)1.Differentialequations,Parabolic.2.Differentialequa
7、tions,Nonlinear.3.Chemicalkinetics—Mathematicalmodels.I.Volpert,VitalyA.,1958–.II.Volpert,VladimirA.,1954–.III.Title.IV.Series.QA377.V64131994515.353—dc2094-16518c1994bytheAmericanMathematicalSociety.Allrightsreserved.TheAmericanMathematicalSocietyretainsall
8、rightsexceptthosegrantedtotheUnitedStatesGovernment.PrintedintheUnitedStatesofAmerica.Reprintedwithcorrections,2000∞Thepaperusedinthisbookisacid-freeandfallswithintheguidelinesest
