Burdeina N. O.
Ukr. Mat. Zh. - 2010. - 62, № 9. - pp. 1173–1199
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.
Classical solvability of a problem with moving boundaries for a hyperbolic system of quasilinear equations
Ukr. Mat. Zh. - 2009. - 61, № 7. - pp. 867-891
Using the method of characteristics and the method of contracting mappings, we establish the local classical solvability of a problem for a hyperbolic system of quasilinear first-order equations with moving boundaries and nonlinear boundary conditions. Under additional assumptions on the monotonicity and sign constancy of initial data and a restriction on the growth of the right-hand sides of the system, we formulate sufficient conditions for the global classical solvability of the problem.