TY  - BOOK
AU  - Doelman,Arjen
AU  - Gardner,Robert A.
AU  - Kaper,Tasso J.
TI  - Stability Index Analysis of 1-D Patterns of the Gray-Scott Model
T2  - Memoirs of the American Mathematical Society
SN  - 9781470403300
AV  - QA377 -- .D64 2002eb 
U1  - 510 s;515/.353 
PY  - 2002///
CY  - Providence
PB  - American Mathematical Society
KW  - Reaction-diffusion equations
KW  - Perturbation (Mathematics)
KW  - Eigenvalues
KW  - Electronic books
N1  - 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&lt -- 1/2 -- 5.2. The Other Regimes: 1/2≤β&lt -- 1 -- Chapter 6. Concluding Remarks -- Bibliography
UR  - https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3114483
ER  -