Establishes spreading-vanishing dynamics in river networks, suggesting threshold behaviors for water flow.
We study the long-time behaviour of solutions to a free boundary model in river networks with small water flow speeds. First, we establish the well-posedness of our model. Under suitable assumptions, we then establish a spreading–vanishing dichotomy result for solutions to our model. By introducing a parameter σ in the initial data, we derive sharp threshold behaviours.
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季迎 et al. (2026) studied this question.
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