Solutions for PDEs with constant coefficients and derivability of functions ranged in commutative algebras

DOI10.1002/mma.3019zbMath1320.35015OpenAlexW2120440418MaRDI QIDQ5256508

Anatoliy A. Pogorui, Michael V. Shapiro, Ramón Martin Rodríguez Dagnino

Publication date: 17 June 2015

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: http://eprints.zu.edu.ua/13298/1/2013-mma.Solution_PDE.pdf

zbMATH Keywords

monogenic functionsalgebra-valued functions

Mathematics Subject Classification ID

General theory of PDEs and systems of PDEs with constant coefficients (35E20) Other special methods applied to PDEs (35A25) Other partial differential equations of complex analysis in several variables (32W50)

Related Items (8)

Hausdorff analytic functions in a three-dimensional associative noncommutative algebra ⋮ Generalized Cauchy-Riemann equations in non-identity bases with application to the algebrizability of vector fields ⋮ Generalized Clifford algebras associated to certain partial differential equations ⋮ On solutions of PDEs by using algebras ⋮ Solutions of some partial differential equations with variable coefficients by properties of monogenic functions ⋮ Monogenic functions in commutative algebras associated with classical equations of mathematical physics ⋮ Solution of systems of partial differential equations by using properties of monogenic functions on commutative algebras ⋮ On monogenic functions defined in different commutative algebras

Cites Work

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• Biharmonic bases in algebras of the second rank
• Symmetry reduction and some exact solutions of nonlinear biwave equations
• One-dimensional semi-Markov evolutions with general Erlang sojourn times
• On the Klein–Gordon equation and hyperbolic pseudoanalytic function theory
• Hyperholomorphic functions on commutative algebras
• Application of an Algebraic Technique to the Solution of Laplace’s Equation in Three Dimensions
• Solution of linear partial differential equations by Lie algebraic methods

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