We consider the first boundary-value problem for a third-order equation with multiple characteristics u xxx − u yy = f(x, y) in a domain D = {(x, y):0 < x < p, 0 < y < l}. The unique solvability of the problem is proved by the method of energy integrals and its explicit solution is constructed by the method of Green functions.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 1, pp. 3–13, January, 2012.
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Apakov, Y.P. On the solution of a boundary-value problem for a third-order equation with multiple characteristics. Ukr Math J 64, 1–12 (2012). https://doi.org/10.1007/s11253-012-0625-1
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DOI: https://doi.org/10.1007/s11253-012-0625-1