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The complex reflection method for some classes of equations with the third derivative distinguished. (Russian, English) Zbl 1052.35050

Sib. Mat. Zh. 45, No. 5, 1073-1085 (2004); translation in Sib. Math. J. 45, No. 5, 883-893 (2004).
The author suggests a method for constructing the Green’s functions for boundary-value problems in “half-space” type domains for some classes of partial differential equations whose third derivative with respect to the first spatial variable is distinguished. He gives formulas for exact solutions and proves uniqueness theorems in the Schwartz spaces.

MSC:

35C15 Integral representations of solutions to PDEs
35Q72 Other PDE from mechanics (MSC2000)
76H05 Transonic flows
35A08 Fundamental solutions to PDEs
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