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On the solutions of a multidimensional differential equation of arbitrary order with mixed higher partial derivatives and power-law nonlinearities. (Russian. English summary) Zbl 1474.35218

Summary: We study the solutions of a multidimensional differential equation of arbitrary order containing mixed higher partial derivatives and power-law nonlinearities in the unknown function and its first derivatives. The method of functional separation of variables is applied for examining this equation. The particular solutions of the equation under consideration are obtained. Some theorems which permit to decrease the order of this equation are proved.

MSC:

35G05 Linear higher-order PDEs
35C05 Solutions to PDEs in closed form
Full Text: MNR

References:

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