Buch, Englisch, 160 Seiten, Format (B × H): 156 mm x 241 mm, Gewicht: 331 g
Reihe: Monographs and Surveys in Pure and Applied Mathematics
Buch, Englisch, 160 Seiten, Format (B × H): 156 mm x 241 mm, Gewicht: 331 g
Reihe: Monographs and Surveys in Pure and Applied Mathematics
ISBN: 978-0-582-31749-9
Verlag: Chapman and Hall/CRC
Clifford analysis represents one of the most remarkable fields of modern mathematics. With the recent finding that almost all classical linear partial differential equations of mathematical physics can be set in the context of Clifford analysis-and that they can be obtained without applying any physical laws-it appears that Clifford analysis itself can suggest new equations or new generalizations of classical equations that may have some physical content.
Partial Differential Equations in Clifford Analysis considers-in a multidimensional space-elliptic, hyperbolic, and parabolic operators related to Helmholtz, Klein-Gordon, Maxwell, Dirac, and heat equations. The author addresses two kinds of parabolic operators, both related to the second-order parabolic equations whose principal parts are the Laplacian and d'Alembertian: an elliptic-type parabolic operator and a hyperbolic-type parabolic operator. She obtains explicit integral representations of solutions to various boundary and initial value problems and their properties and solves some two-dimensional and non-local problems.
Written for the specialist but accessible to non-specialists as well, Partial Differential Equations in Clifford Analysis presents new results, reformulations, refinements, and extensions of familiar material in a manner that allows the reader to feel and touch every formula and problem. Mathematicians and physicists interested in boundary and initial value problems, partial differential equations, and Clifford analysis will find this monograph a refreshing and insightful study that helps fill a void in the literature and in our knowledge.
Zielgruppe
Professional
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
IntroductionPrinciples of Clifford Algebra and AnalysisThe Basic Notions and DefinitionsMatrix Representations of Clifford Algebras for any DimensionDifferential Operators and ClassificationLorentz Transformations in the Elliptic and Hyperbolic CasesElliptic Partial Differential EquationsIntroductionCauchy Kernel and Representations for h-regular Functions in R(n)Extension Theorems and The Riemann-Schwarz Principle of ReflectionThe Poincaré-Bertrand Transformation FormulaGeneralized Riesz SystemThe Basic L-Theory of the Fourier Integral TransformationBoundary Value Problems for Regular Functions with Values in R(n)Boundary Value Problems for h-Regular Functions with Values in R(n), n³1The Beltrami Equation in R(n)Hyperbolic Partial Differential EquationsIntroductionGeneralized Maxwell and Dirac EquationsThe Hyperbolic Beltrami EquationInitial Value Problems for the Klein-Gordon EquationCauchy's Initial Value Problem and its Modification for the Regular and h-Regular Functions with Values in R(n,n-1) and in R(n,n-2), n³3Parabolic Partial Differential EquationsIntroductionParabolic Regular System of the First KindInitial Value Problems for Parabolic Equations of the First KindParabolic Regular Equations of the Second Kind and Initial Value ProblemsEffective Solutions for Some Non-Local ProblemsIntroductionWiener-Hopf and Dual Integral Equations of Convolution TypeGeneralized Wiener-Hopf Integral Equation with Two Kernels Depending on the Difference and Sum of the ArgumentsDual Integral Equations with Kernels Depending on the Difference and Sum of ArgumentsNon-Local Problems for Holomorphic Functions and Applications in Elasticity TheoryNon-Local Problems for Generalized Holomorphic Functions and the Generalized Beltrami EquationNon-Local Problems for Polyharmonic FunctionsEpilogueBibliography
