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AuthorObolashvili, Elena. author
TitleHigher Order Partial Differential Equations in Clifford Analysis [electronic resource] : Effective Solutions to Problems / by Elena Obolashvili
ImprintBoston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 2003
Connect tohttp://dx.doi.org/10.1007/978-1-4612-0015-4
Descript IX, 178 p. online resource

SUMMARY

The most important thing is to write equations in a beautiful form and their success in applications is ensured. Paul Dirac The uniqueness and existence theorems for the solutions of boundary and initial value problems for systems of high-order partial differential equations (PDE) are sufficiently well known. In this book, the problems considered are those whose solutions can be represented in quadratures, i.e., in an effective form. Such problems have remarkable applications in mathematical physics, the mechanics of deformable bodies, electroยญ magnetism, relativistic quantum mechanics, and some of their natural generalizations. Almost all such problems can be set in the context of Clifford analysis. Moreover, they can be obtained without applying any physical laws, a circumstance that gives rise to the idea that Clifford analysis itself can suggest generalizations of classical equations or new equations altogether that may have some physical content. For that reason, Clifford analysis represents one of the most remarkable fields in modem mathematics as well as in modem physics


CONTENT

I Boundary Value Problems for Regular, Generalized Regular and Pluriregular Elliptic Equations -- I Two-Dimensional Cases -- II Multidimensional Cases -- II Initial Value Problems for Regular and Pluriregular, Hyperbolic and Parabolic Equations -- III Hyperbolic and Plurihyperbolic Equations in Clifford Analysis -- IV Parabolic and Pluriparabolic Equations in Clifford Analysis -- Epilogue -- References


Mathematics Partial differential equations Applied mathematics Engineering mathematics Differential geometry Physics Mathematics Partial Differential Equations Applications of Mathematics Differential Geometry Theoretical Mathematical and Computational Physics



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