# memo_has_moved_text();The Role of Advection in a Two-Species Competition Model: A Bifurcation Approach

Isabel Averill, King-Yeung Lam and Yuan Lou

Publication: Memoirs of the American Mathematical Society
Publication Year: 2017; Volume 245, Number 1161
ISBNs: 978-1-4704-2202-8 (print); 978-1-4704-3611-7 (online)
DOI: https://doi.org/10.1090/memo/1161
Published electronically: July 26, 2016
Keywords:Reaction-diffusion, advection, evolution of dispersal, principal eigenvalue, global bifurcation

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Chapters

• Chapter 1. Introduction: The role of advection
• Chapter 2. Summary of main results
• Chapter 3. Preliminaries
• Chapter 4. Coexistence and classification of $\mu$-$\nu$ plane
• Chapter 5. Results in $\mathcal R_1$: Proof of Theorem 2.10
• Chapter 6. Results in $\mathcal R_2$: Proof of Theorem 2.11
• Chapter 7. Results in $\mathcal R_3$: Proof of Theorem 2.12
• Chapter 8. Summary of asymptotic behaviors of $\eta _*$ and $\eta ^*$
• Chapter 9. Structure of positive steady states via Lyapunov-Schmidt procedure
• Chapter 10. Non-convex domains
• Chapter 11. Global bifurcation results
• Chapter 12. Discussion and future directions
• Appendix A. Asymptotic behavior of $\tilde u$ and $\lambda _u$
• Appendix B. Limit eigenvalue problems as $\mu ,\nu \to 0$
• Appendix C. Limiting eigenvalue problem as $\mu \to \infty$