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.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 7, pp. 867–891, July, 2009.
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Andrusyak, R.V., Burdeina, N.O. & Kyrylych, V.M. Classical solvability of a problem with moving boundaries for a hyperbolic system of quasilinear equations. Ukr Math J 61, 1025–1054 (2009). https://doi.org/10.1007/s11253-009-0269-y
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DOI: https://doi.org/10.1007/s11253-009-0269-y