Using the method of contracting mappings, we prove, for small values of time, the existence and uniqueness of a generalized Lipschitz solution of a mixed problem with unknown boundaries for a hyperbolic quasilinear system of first-order equations represented in terms of Riemann invariants with nonlocal (nonseparated and integral) boundary conditions.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 9, pp. 1173–1199, September, 2010.
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Andrusyak, R.V., Burdeina, N.O. & Kyrylych, V.M. Quasilinear hyperbolic stefan problem with nonlocal boundary conditions. Ukr Math J 62, 1367–1396 (2011). https://doi.org/10.1007/s11253-011-0437-8
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DOI: https://doi.org/10.1007/s11253-011-0437-8