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The Role of Advection in a Two-Species Competition Model.
The effects of weak and strong advection on the dynamics of reaction-diffusion models have long been studied. In contrast, the role of intermediate advection remains poorly understood. For example, concentration phenomena can occur when advection is strong, providing a mechanism for the coexistence...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence :
American Mathematical Society,
2017.
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| Colección: | Memoirs of the American Mathematical Society.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Title page; Chapter 1. Introduction: The role of advection; Chapter 2. Summary of main results; 2.1. Existence of positive steady states of (2.1); 2.2. Local stability of semi-trivial steady states; 2.3. Global bifurcation results; Chapter 3. Preliminaries; 3.1. Abstract Theory of Monotone Dynamical Systems; 3.2. Asymptotic behavior of and as →0; Chapter 4. Coexistence and classification of
- plane; 4.1. Coexistence: Proof of Theorem 2.2; 4.2. Classification of
- plane: Proof of Theorem 2.5; 4.3. Limiting behavior of ; Chapter 5. Results in ℛ₁: Proof of Theorem 2.10
- 5.1. The case when ( , )∈ℛ₁ and ( )/( ) is sufficiently large5.2. The one-dimensional case; 5.3. Open problems; Chapter 6. Results in ℛ₂: Proof of Theorem 2.11; 6.1. Proof of Theorem 2.11(b); 6.2. Open problems; Chapter 7. Results in ℛ₃: Proof of Theorem 2.12; 7.1. Stability result of ( ,0) for small ; 7.2. Stability result of (0, ); 7.3. Open problems; Chapter 8. Summary of asymptotic behaviors of _{*} and *; 8.1. Asymptotic behavior of *; 8.2. Asymptotic behavior of _{*}; Chapter 9. Structure of positive steady states via Lyapunov-Schmidt procedure
- Chapter 10. Non-convex domainsChapter 11. Global bifurcation results; 11.1. General bifurcation theorems; 11.2. Bifurcation result in ℛ₁; 11.3. Bifurcation result in ℛ₃; 11.4. Bifurcation result in ℛ₂; 11.5. Uniqueness result for large , ; Chapter 12. Discussion and future directions; Appendix A. Asymptotic behavior of and ᵤ; A.1. Asymptotic behavior of when →∞; A.2. Asymptotic behavior of and its derivatives as →0; A.3. Asymptotic behavior of ᵥ as , →∞; Appendix B. Limit eigenvalue problems as , →0; Appendix C. Limiting eigenvalue problem as →∞; Acknowledgements