On solutions of a discretized heat equation in discrete Clifford analysis. (English) Zbl 1283.39002
Summary: The main purpose of this paper is to study solutions of the heat equation in the setting of discrete Clifford analysis. More precisely, we consider this equation with discrete space and continuous time. Thereby, we focus on representations of solutions by means of dual Taylor series expansions. Furthermore, we develop a discrete convolution theory, apply it to the inhomogeneous heat equation and construct solutions for the related Cauchy problem by means of heat polynomials.
MSC:
| 39A12 | Discrete version of topics in analysis |
| 35K05 | Heat equation |
| 15A66 | Clifford algebras, spinors |
| 35K08 | Heat kernel |
Keywords:
heat equation; heat kernel; discrete Clifford analysis; dual Taylor series expansions; Cauchy problem; heat polynomialReferences:
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