TY  - BOOK
AU  - Wang,Kelei
ED  - SpringerLink (Online service)
TI  - Free Boundary Problems and Asymptotic Behavior of Singularly Perturbed Partial Differential Equations
T2  - Springer Theses, Recognizing Outstanding Ph.D. Research,
SN  - 9783642336966
AV  - QA370-380 
U1  - 515.353 23
PY  - 2013///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg, Imprint: Springer
KW  - Mathematics
KW  - Functional analysis
KW  - Partial differential equations
KW  - Partial Differential Equations
KW  - Functional Analysis
N1  - 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
N2  - 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
UR  - http://dx.doi.org/10.1007/978-3-642-33696-6
ER  -