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Solution of systems of partial differential equations by using properties of monogenic functions on commutative algebras. (English. Ukrainian original) Zbl 1441.30074
J. Math. Sci., New York 239, No. 1, 43-50 (2019); translation from Ukr. Mat. Visn. 15, No. 2, 210-219 (2018).
Summary: Some systems of differential equations with partial derivatives are studied by using the properties of Gâteaux differentiable functions on commutative algebras. The connection between solutions of systems of partial differential equations and components of monogenic functions on the corresponding commutative algebras is shown. We also give some examples of systems of partial differential equations and find their solutions.
MSC:
30G35 Functions of hypercomplex variables and generalized variables
32W50 Other partial differential equations of complex analysis in several variables
35G05 Linear higher-order PDEs
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