Abstract
By using the method of characteristics, we investigate the well-posedness of local problems (Cauchy problem and mixed problems) and nonlocal problems (with nonseparable and integral conditions) for some multidimensional almost-linear hyperbolic systems of the first order. We reduce these problems to systems of integro-operator equations and prove theorems on the existence and uniqueness of classical solutions.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 2, pp. 192–203, February, 2008.
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Kmit’, I.Y., Ptashnyk, B.I. Well-posedness of boundary-value problems for multidimensional hyperbolic systems. Ukr Math J 60, 221–234 (2008). https://doi.org/10.1007/s11253-008-0054-3
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DOI: https://doi.org/10.1007/s11253-008-0054-3