Free Boundary Problems and Asymptotic Behavior of Singularly Perturbed Partial Differential Equations

Kelei Wang

ISBN 10: 3642336957 / ISBN 13: 9783642336959

Editore: Springer Berlin Heidelberg, 2012

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Druck auf Anfrage Neuware - Printed after ordering - 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 these two problems. We study the free boundary problems in the singulary 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. 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.

Codice articolo 9783642336959

Dati bibliografici

• Titolo: Free Boundary Problems and Asymptotic Behavior of Singularly Perturbed Partial Differential Equations
• Editore: Springer Berlin Heidelberg
• Data di pubblicazione: 2012
• Lingua: Inglese
• ISBN 10: 3642336957
• ISBN 13: 9783642336959
• Rilegatura: Buch
• Condizione: Neu
• Dimensioni: 241 L x 160 A x 12 P (millimetri) 241 millimetri di larghezza per 160 millimetri di altezza per 12 millimetri di profondità
• Peso: 360 grammi

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Riassunto

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 these two problems. We study the free boundary problems in the singulary 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.

Dalla quarta di copertina

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.