Quasilinear hyperbolic stefan problem with nonlocal boundary conditions
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.
English version (Springer): Ukrainian Mathematical Journal 62 (2010), no. 9, pp 1367-1396.
Citation Example: Andrusyak R. V., Burdeina N. O., Kirilich V. M. Quasilinear hyperbolic stefan problem with nonlocal boundary conditions // Ukr. Mat. Zh. - 2010. - 62, № 9. - pp. 1173–1199.