Classical solvability of a problem with moving boundaries for a hyperbolic system of quasilinear equations
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.
English version (Springer): Ukrainian Mathematical Journal 61 (2009), no. 7, pp 1025-1054.
Citation Example: Andrusyak R. V., Burdeina N. O., Kirilich V. M. Classical solvability of a problem with moving boundaries for a hyperbolic system of quasilinear equations // Ukr. Mat. Zh. - 2009. - 61, № 7. - pp. 867-891.