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Higher Order Partial Differential Equations in Clifford Analysis

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Higher Order Partial Differential Equations in Clifford Analysis Cover

 

Synopses & Reviews

Publisher Comments:

This monograph is devoted to new types of higher order PDEs in the framework of Clifford analysis. While elliptic and hyperbolic equations have been studied in the Clifford analysis setting in book and journal literature, parabolic equations in this framework have been largely ignored and are the primary focus of this work. Thus, new types of equations are examined: elliptic-hyperbolic, elliptic-parabolic, hyperbolic-parabolic and elliptic-hyperbolic-parabolic. These equations are related to polyharmonic, polywave, polyheat, harmonic-wave, harmonic-heat, wave-heat and harmonic-wave-heat equations for which various boundary and initial value problems are solved explicitly in quadratures. The solutions to these new equations in the Clifford setting have some remarkable applications, for example, to the mechanics of deformable bodies, electromagnetic fields, and quantum mechanics.

Table of Contents

Introduction.- Part I: Boundary Value Problems for Regular, Generalized, Regular and Pluriregular Elliptic Equations.- Two Dimensional Cases; Multi-Dimensional Cases.- Part II: Initial Value Problems for Regular, Pluriregular Hyperbolic and Parabolic Equations.- Hyperbolic and Plurihyperbolic Equations in Clifford Analysis; Parabolic and Pluriparabolic Equations in Clifford Analysis; Epilogue.- References.- Index.

Product Details

ISBN:
9780817642860
Author:
Obolashvili, Elena
Publisher:
Birkhauser
Author:
Obolashvili, E. I.
Author:
Obolashvili, F.
Subject:
General
Subject:
Differential Equations - Partial Differential Equations
Subject:
Differential equations, Parabolic
Subject:
Clifford algebras
Subject:
General-General
Publication Date:
20021031
Binding:
Hardcover
Language:
English
Illustrations:
Y
Pages:
178
Dimensions:
9.02x6.76x.68 in. 1.08 lbs.

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Related Subjects


Science and Mathematics » Mathematics » Applied
Science and Mathematics » Mathematics » Differential Equations
Science and Mathematics » Mathematics » Geometry » Algebraic Geometry

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