Demonstrates distinct solution types for the one-dimensional Stefan problem, indicating initial function size importance.
We study the one-dimensional one-phase Stefan problem for the heat equation with a nonlinear boundary condition. We show that all solutions fall into one of three distinct types: global-in-time solutions with exponential decay, global-in-time solutions with non-exponential decay, and finite-time blow-up solutions. The classification depends on the size of the initial function. Furthermore, we describe the behavior of solutions at the blow-up time.
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Araya et al. (2026) studied this question.
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