In Part I of this monograph, we develop, via the method of matched asymptotic expansions (MAE), a rational approach to obtaining the complete large-t (dimensionless time) structure of the solution to initial-boundary value problems (IBVPs) and initial value problems (IVPs) for reaction-diffusion equations of the Fisher-Kolmogorov type, which exhibit the formation of a permanent form travelling wave (PTW) structure. In particular, this approach allows the wave speed for the large-t PTW, the correction to the wave speed and the rate of convergence of the solution of the IBVP or IVP onto the PTW to be determined. This large-t structure is obtained by careful consideration of the asymptotic structures as t→ 0 (0 ≤ x < ∞) (where x is the dimensionless distance) and as x→ ∞ (t ≥ O(1)).
KeywordsWave Front Wave Speed Propagation Speed Reaction Function Matched Asymptotic Expansion
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