03387nam 2200601Ia 450 991043814600332120200520144314.01-283-91080-23-642-33696-510.1007/978-3-642-33696-6(CKB)2670000000317386(EBL)1082714(OCoLC)823388571(SSID)ssj0000878934(PQKBManifestationID)11479440(PQKBTitleCode)TC0000878934(PQKBWorkID)10850867(PQKB)10412346(DE-He213)978-3-642-33696-6(MiAaPQ)EBC1082714(PPN)168325195(EXLCZ)99267000000031738620121227d2013 uy 0engur|n|---|||||txtccrFree boundary problems and asymptotic behavior of singularly perturbed partial differential equations /Kelei Wang1st ed. 2013.Berlin ;Heidelberg Springerc20131 online resource (116 p.)Springer theses,2190-5053Description based upon print version of record.3-642-44248-X 3-642-33695-7 Includes bibliographical references and index.Foreword -- Acknowledgements -- Introduction -- Uniqueness, Stability and Uniform Lipschitz Estimates -- Uniqueness in the Singular Limit -- The Dynamics of One Dimensional Singular Limiting Problem.- Approximate Clean Up Lemma.- Asymptotics in Strong Competition -- The Limited Equation of a Singular Perturbed System -- Reference -- Index.In Bose-Einstein condensates from physics and competing species system from population dynamics, it is observed that different condensates (or species) tend to be separated. This is known as the phase separation phenomena. These pose a new class of free boundary problems of nonlinear partial differential equations. Besides its great difficulty in mathematics, the study of this problem will help us get a better understanding of the phase separation phenomena. This thesis is devoted to the study of the asymptotic behavior of singularly perturbed partial differential equations and some related free boundary problems arising from Bose-Einstein condensation theory and competing species model. We study the free boundary problems in the singular limit and give some characterizations, and use this to study the dynamical behavior of competing species when the competition is strong. These results have many applications in physics and biology.   It was nominated by the Graduate University of Chinese Academy of Sciences as an outstanding PhD thesis.Springer Theses, Recognizing Outstanding Ph.D. Research,2190-5053Boundary value problemsAsymptotic theoryDifferential equations, PartialAsymptotic theoryBoundary value problemsAsymptotic theory.Differential equations, PartialAsymptotic theory.515.353Wang Kelei1058835MiAaPQMiAaPQMiAaPQBOOK9910438146003321Free Boundary Problems and Asymptotic Behavior of Singularly Perturbed Partial Differential Equations2502699UNINA