Higher-order partial differential equations in Clifford analysis. Effective solutions to problems
Boundary value problems (BVP) and initial -BVP for systems of PDE for canonical domains are solved in the book. One of the typical equations has the form \(( \Delta -\frac{\partial ^{2}}{\partial t^{2}}) ( \Delta -\frac{\partial }{\partial \tau } u(x,t,\tau )=0\). The solutions of the problems has been obtained in closed form. The book contains many interesting formulas for solutions of BVP, mainly for the half-space. The author does not cite [\textit{È. I. Zverovich}, Russ. Math. Surv. 26 (1971), No. 1, 117--192 (1972); translation from Usp. Mat. Nauk 26, No.1(157), 113--179 (1971; Zbl 0217.10201)] and [\textit{V. V. Mityushev} and \textit{S. V. Rogosin}, Constructive methods for linear and nonlinear boundary value problems for analytic functions: theory and applications (2000; Zbl 0957.30002)], where some problems for harmonic and biharmonic functions are solved in more general statements. Contents of the book: Part I. BVP for regular, generalized regular and pluriregular elliptic equations. 1. Two-dimensional case. BVP for classical and generalized Beltrami equations, for plurigeneralized holomorphic, polyharmonic, polymetaharmonic functions etc. are solved. 2. Multidimensional cases. Elements of Clifford analysis are presented. BVP for poly-Helmholtz, pluri-Beltrami equations etc. in Clifford analysis are solved. Part II. Initial value problems for regular and pluriregular hyperbolic and parabolic equations. 3. Hyperbolic and plurihyperbolic equations in Clifford analysis. 4. Parabolic and pluriparabolic equations in Clifford analysis.
scientific article; zbMATH DE number 1862426
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