| Principles of Partial Differential Equations 2010 Edition Contributor(s): Komech, Alexander (Author), Komech, Andrew (Author) |
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ISBN: 1441910956 ISBN-13: 9781441910950 Publisher: Springer OUR PRICE: $56.99 Product Type: Hardcover - Other Formats Published: October 2009 |
| Additional Information |
| BISAC Categories: - Mathematics | Differential Equations - Partial - Mathematics | Mathematical Analysis |
| Dewey: 515.353 |
| LCCN: 2009932894 |
| Series: Problem Books in Mathematics |
| Physical Information: 0.44" H x 6.14" W x 9.21" (0.92 lbs) 161 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: ThisbookisintendedtogivethereaderanopportunitytomastersolvingPDEpr- lems. Ourmaingoalwastohaveaconcisetextthatwouldcovertheclassicaltools ofPDEtheorythatareusedintoday'sscienceandengineering, suchaschar- teristics, thewavepropagation, theFouriermethod, distributions, Sobolevspaces, fundamentalsolutions, andGreen'sfunctions. WhileintroductoryFouriermethod -basedPDEbooksdonotgiveanadequatedescriptionoftheseareas, themore advancedPDEbooksarequitetheoreticalandrequireahighlevelofmathematical backgroundfromareader. Thisbookwaswrittenspeci?callyto?llthisgap, sat- fyingthedemandofthewiderangeofenduserswhoneedtheknowledgeofhow tosolvethePDEproblemsandatthesametimearenotgoingtospecializeinthis areaofmathematics. Arguably, thisistheshortestPDEcourse, whichstretchesfar beyondcommon, Fouriermethod-basedPDEtexts. Forexample, [Hab03], which isacommonthoroughtextbookonpartialdifferentialequations, teachesasimilar setoftoolswhilebeingabout?vetimeslonger. Thebookisproblem-oriented. Thetheoreticalpartisrigorousyetshort. So- timeswereferthereadertotextbooksthatgivewidercoverageofthetheory. Yet, - portanttheoreticaldetailsarepresentedwithcare, whilethehintsgivethereaderan opportunitytorestoretheargumentstothefullrigor. Manyexamplesfromphysics areintendedtokeepthebookintuitiveforthereaderandtoillustratetheapplied natureofthesubject. Thebookwillbeusefulforanyhigher-levelundergraduatecourseandforse- studyforbothgraduateandhigher-levelundergraduatestudents, andforanys- cialtyinsciences. ItsRussianversionhasbeenastandardproblem-solvingmanual atMoscowStateUniversitysince1988, andisalsousedbystudentsofSt. Pete- burgUniversityandNovosibirskUniversities. ItsSpanishversionisusedatMorelia UniversityinMexico, whiletheEnglishdrafthasalreadybeenusedinViennaU- versityandatTexasA&MUniversity. Forfurtherreadingwerecommend[Str92], [Eva98], and[EKS99]. Mu]nchen, AlexanderKomech August2007 AndrewKomech v Acknowledgements The?rstauthorisindebtedtoMargaritaKorotkinaforthefortunatesuggestionto writethisbook, toA. F. Filippov, A. S. Kalashnikov, M. A. Shubin, T. D. Ventzel, andM. I. Vishikforcheckingthe?rstversionofthemanuscriptandfortheadvice. BothauthorsaregratefultoH. Spohn(TechnischeUniversita]t, Mu]nchen)andto E. Zeidler(Max-PlanckInstituteforMathematics, Leipzig)fortheirhospitalityand supportduringtheworkonthebook. BothauthorsweresupportedbyInstituteforInformationTransmissionProblems (RussianAcademyofSciences). The?rstauthorwassupportedbytheDepartment ofMechanicsandMathematicsofMoscowStateUniversity, bytheAlexandervon HumboldtResearchAward, FWFGrantP19138-N13, andtheGrantsofRFBR. The secondauthorwassupportedbyTexasA&MUniversityandbytheNationalScience FoundationunderGrantsDMS-0621257andDMS-0600863. vii Contents 1 Hyperbolicequations. Methodofcharacteristics. . . . . . . . . . . . . . . . . . . 1 1 Derivationofthed'Alembertequation. . . . . . . . . . . . . . . . . . . . . . . . . 1 2 Thed'Alembertmethodforin?nitestring . . . . . . . . . . . . . . . . . . . . . . 7 3 Analysisofthed'Alembertformula. . . . . . . . . . . . . . . . . . . . . . . . . . . 12 4 Second-orderhyperbolicequationsintheplane . . . . . . . . . . . . . . . . . 19 5 Semi-in?nitestring. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 6 Finitestring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 7 Waveequationwithmanyindependentvariables . . . . . . . . . . . . . . . . 46 8 Generalhyperbolicequations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 2 TheFouriermethod. . . . |