Differential Operators Associated to the Cauchy-Fueter Operator in Quaternion Algebra |
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| Authors: | Thanh Van Nguyen |
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| Institution: | 1. Faculty of Mathematic, Mechanics and Informatics, Hanoi University of Science, 334 Nguyen Trai, Thanh Xuan, Hanoi, Vietnam
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| Abstract: | This paper deals with the initial value problem of the type ${\frac{\partial{w}}{\partial{t}}}=L\left(t,x,w,{\frac{\partial{w}}{\partial{x_i}}}\right)\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad(1)$ $w(0,x)=\varphi(x)\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad(2)$ where t is the time, L is a linear first order operator (matrix-type) in Quaternionic Analysis and ${\varphi}This paper deals with the initial value problem of the type
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\frac?w?t=L(t,x,w,\frac?w?xi) (1){\frac{\partial{w}}{\partial{t}}}=L\left(t,x,w,{\frac{\partial{w}}{\partial{x_i}}}\right)\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad(1) |
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