Author | Obolashvili, Elena. author |
---|---|

Title | Higher Order Partial Differential Equations in Clifford Analysis [electronic resource] : Effective Solutions to Problems / by Elena Obolashvili |

Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 2003 |

Connect to | http://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