Stability Index Analysis of 1-D Patterns of the Gray-Scott Model.
- 1st ed.
- 1 online resource (82 pages)
- Memoirs of the American Mathematical Society ; v.155 .
- Memoirs of the American Mathematical Society .
Intro -- Contents -- Preface -- Chapter 1. Introduction -- 1.1. The Gray-Scott Model: Background -- 1.2. Asymptotic Analysis of the Wave -- 1.3. The Nonlocal Eigenvalue Problem (NLEP) -- 1.4. The Main Results -- Chapter 2. The Evans Function and the Stability Index -- 2.1. The Linearized Equations -- 2.2. The Evans Function -- 2.3. The Stability Index -- 2.4. Outline and Endgame of the Proof -- Chapter 3. Tracking the Fast Subbundle -- 3.1. Asymptotic and Reduced Equations in the Fast Scaling -- 3.2. A Large λ Estimate -- 3.3. Invariant Sets for the Projectivized Flow -- 3.4. Corollaries of the Fast Tracking Theorem -- Chapter 4. The Slow Subbundle -- 4.1. Definition of the Slow Solution -- 4.2. Tracking the Slow Solution over the Slow Fields -- 4.3. Tracking the Slow Solution over the Fast Field -- 4.4. The Construction of ε[sub(8)] (K,δ) -- Chapter 5. Calculation of the Stability Index -- 5.1. The Strongly Unstable Regime: 0≤β< -- 1/2 -- 5.2. The Other Regimes: 1/2≤β< -- 1 -- Chapter 6. Concluding Remarks -- Bibliography.