Solution of Systems of Partial Differential Equations by Using Properties of Monogenic Functions on Commutative Algebras
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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.
KeywordsPDE systems monogenic functions Gâteaux derivative commutative algebra
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- 4.I. P. Melnychenko and S. A. Plaksa, Commutative Algebras and Spatial Potential Fields [in Russian], Institute of Mathematics of th NAS of Ukraine, Kiev, 2008.Google Scholar