Standing Waves for Phase Transitions in a Spherically Symmetric Nozzle

We study the existence of standing waves for liquid/vapor phase transition in a spherically symmetric nozzle. The system is singularly perturbed and the solution consists of an internal layer where the liquid quickly becomes vapor. Using methods from dynamical systems theory, we prove the existence of the internal layer as a heteroclinic orbit connecting the liquid state to the vapor state. The heteroclinic orbit is reproduced numerically and is also shown numerically to be a transversal heteroclinic orbit. The proof of the existence of an exact standing wave solution near the singular limit is based on the geometric singular perturbation theory and is outlined in the paper.

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