Higher Order Partial Differential Equations in Clifford Analysis

Obolashvili, Elena

ISBN 10: 0817642862 / ISBN 13: 9780817642860

Verlag: Birkhäuser Boston, 2002

Beschreibung

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Bestandsnummer des Verkäufers Q-0817642862

Bibliografische Details

• Titel: Higher Order Partial Differential Equations in Clifford Analysis
• Verlag: Birkhäuser Boston
• Erscheinungsjahr: 2002
• Sprache: Englisch
• ISBN-10: 0817642862
• ISBN-13: 9780817642860
• Einband: Hardcover
• Zustand: New
• Gewicht: 17 Unzen

Über diesen Titel

Inhaltsangabe

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.

Reseña del editor

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. This book will appeal to mathematicians and physicists in PDEs who are interested in boundary and initial value problems, and may be used as a supplementary text by graduate students.