This research investigates pattern formation in diffusion models, revealing unique solutions and behaviors in varying conditions.
In this paper, we investigate the pattern formation in reaction–diffusion models with degenerate diffusion and spatially heterogeneous coefficients. By analyzing both local and nonlocal dispersal formulations, we establish precise conditions for the existence, uniqueness, and asymptotic behavior of positive and semipositive solutions. Our results demonstrate that the combined degeneracies in diffusion and reaction fundamentally reshape the solution structure, giving rise to multiple nonnegative solutions, distinct blow‐up profiles, and extended parameter regimes for existence.
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Sun et al. (2026) studied this question.
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