Opuscula Math. 43, no. 4 (2023), 475-491

Opuscula Mathematica

The heat equation on time scales

Tom Cuchta
Rui A.C. Ferreira

Abstract. We present the use of a Fourier transform on time scales to solve a dynamic heat IVP. This is done by inverting a certain exponential function via contour integral. We include some specific examples and directions for further study.

Keywords: heat equation, time scales, Fourier transform.

Mathematics Subject Classification: 39A14, 34N05, 42A38.

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  • Tom Cuchta
  • Department of Mathematics, Marshall University, 1 John Marshall Drive, Huntington, WV 25755 USA
  • Rui A.C. Ferreira (corresponding author)
  • Grupo Física-Matemática, Departamento de Matemática, Faculdade de Ciências, Universidade de Lisboa, Av. Prof. Gama Pinto, 2, 1649-003 Lisboa, Portugal
  • Communicated by Petr Stehlík.
  • Received: 2022-11-02.
  • Revised: 2023-03-24.
  • Accepted: 2023-04-13.
  • Published online: 2023-06-13.
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Cite this article as:
Tom Cuchta, Rui A.C. Ferreira, The heat equation on time scales, Opuscula Math. 43, no. 4 (2023), 475-491, https://doi.org/10.7494/OpMath.2023.43.4.475

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