Analysis of a reaction-diffusion equation shows conditions for blow-up and vanishing solutions, indicating important dynamics in mathematical modeling.
This paper concerns the dynamics of a reaction-diffusion equation with an exponential nonlocal reaction term and free boundaries in one-dimensional space. We first give some sufficient conditions of the finite time blow-up and vanishing of the solution. Then, a sharp threshold trichotomy result for distinguishing blow-up, vanishing, and transition solutions is established.
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Shi et al. (2025) studied this question.
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