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Initial Value Problems in Quaternionic Analysis with a Disturbed Dirac Operator

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Abstract

Initial value problems (IVPs) of type

$$\frac{\partial u}{\partial t} = L ( t, x, u, \frac{\partial u}{\partial x_j} ), \quad u(0, x) = \varphi (x)$$

can be solved by applying the method of associated spaces which is constructed by W.Tutschke (Teubner Leipzig and Springer-Verlag 1989). The present paper considers above IVPs in the space of Helmholtz-type generalized regular functions in the sense of quaternionic analysis. Using the Poisson integral formula, we shall prove an interior estimate for Helmholtz-type generalized regular functions and then give out conditions under which these IVPs are uniquely solvable.

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Authors and Affiliations

  1. School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, No. 1 Road Dai Co Viet, Hanoi, Vietnam

    Nguyen Quoc Hung

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  1. Nguyen Quoc Hung
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Correspondence to Nguyen Quoc Hung.

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Hung, N.Q. Initial Value Problems in Quaternionic Analysis with a Disturbed Dirac Operator. Adv. Appl. Clifford Algebras 22, 1061–1068 (2012). https://doi.org/10.1007/s00006-012-0332-x

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  • DOI: https://doi.org/10.1007/s00006-012-0332-x

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