🎬how the shape and peak height change for pure diffusion and pure decay and the combined scenario

The experimental doubling of both the Diffusivity ( $D$ ) and the Decay Rate ( $\lambda$ ) clearly demonstrated their independent and accelerated control over the reaction-diffusion system. The higher $D$ drastically speeds up the spatial redistribution, causing the concentration peak to flatten and spread across the domain in roughly half the original time, while conserving the existing mass. Simultaneously, the higher $\lambda$ dictates the system's temporal lifespan, causing the entire profile to shrink exponentially downwards at a much faster rate, acting as an accelerated mass sink. In the combined scenario, the decay mechanism's rapid destruction of the material means that while the concentration peak spreads quickly, the overall mass vanishes before it can diffuse extensively to the domain boundaries, confirming that the decay rate ultimately dominates the total existence time of the material.

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Derivation of the Diffusion and Heat Equations from the Continuity Principle | Condensed Notesviadean on Notion