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On the solution of a boundary-value problem for a third-order equation with multiple characteristics. (English. Russian original) Zbl 1258.35064

Ukr. Math. J. 64, No. 1, 1-12 (2012); translation from Ukr. Mat. Zh. 64, No. 1, 3-13 (2012).
Summary: 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.

MSC:

35G15 Boundary value problems for linear higher-order PDEs
35A08 Fundamental solutions to PDEs
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References:

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