Quasilinear hyperbolic stefan problem with nonlocal boundary conditions - Andrusyak, R. V.; Burdeina, N. O.; Kirilich, V. M. (Ukrains’kyi Matematychnyi Zhurnal, 2010)
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.