Synopses & Reviews
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.