Higher Order Partial Differential Equations in Clifford Analysis
Effective Solutions to Problems
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Beschreibung
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, electro 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.
New types of parabolic equations of high order considered in the Clifford analysis framework Pluri-Beltrami and plurigeneralized Beltrami equations for ellpitic and hyperbolic cases Boundary and initial value problems solved in quadratures
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 have been ignored and are the primary focus of this work. These new equations have remarkable applications to mathematical physics---mechanics of deformable bodies, electromagnetic fields, quantum mechanics. Book will appeal to mathematicians and physicists in PDEs, and it may also be used as a supplementary text by graduate students.
Autor*in
Elena Obolashvili
Themen in »Higher Order Partial Differential Equations in Clifford Analysis«
Applications of Mathematics Boundary value problem Clifford Analysis Partial Differential Equations hyperbolic equation partial differential equation