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On reduction of some classes of partial differential equations to equations with fewer variables and exact solutions. (Russian, English) Zbl 1150.35345

Sib. Mat. Zh. 47, No. 4, 791-797 (2006); translation in Sib. Math. J. 47, No. 4, 653-658 (2006).
Summary: We establish a connection between the fundamental solutions to some classes of linear nonstationary partial differential equations and the fundamental solutions to other nonstationary equations with fewer variables. In particular, reduction enables us to obtain exact formulas for the fundamental solutions of some spatial nonstationary equations of mathematical physics (for example, the Kadomtsev–Petviashvili equation, the Kelvin–Voigt equation, etc.) from the available fundamental solutions to one-dimensional stationary equations.

MSC:

35E05 Fundamental solutions to PDEs and systems of PDEs with constant coefficients
35Q35 PDEs in connection with fluid mechanics
35G05 Linear higher-order PDEs
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