Solutions to Diffusion-Wave Equation in a Body with a Spherical Cavity under Dirichlet Boundary Condition

Authors

  • Yuriy POVSTENKO Jan Dlugosz University

DOI:

https://doi.org/10.11121/ijocta.01.2011.0035

Keywords:

Diffusion-wave equation, Laplace transform, Fourier transform, Legendre transform, Weber transform, Mittag-Leffler function

Abstract

Solutions to time-fractional diffusion-wave equation with a source term in spherical coordinates are obtained for an infinite medium with a spherical cavity. The solutions are found using the Laplace transform with respect to time t, the finite Fourier transform with respect to the angular coordinate Ï•, the Legendre transform with respect to the spatial coordinate μ, and the Weber transform of the order n+1/2 with respect to the radial coordinate r. In the central symmetric case with one spatial coordinate r the obtained results
coincide with those studied earlier.

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Published

2011-06-27
CITATION
DOI: 10.11121/ijocta.01.2011.0035
Published: 2011-06-27

How to Cite

POVSTENKO, Y. (2011). Solutions to Diffusion-Wave Equation in a Body with a Spherical Cavity under Dirichlet Boundary Condition. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 1(1), 3–16. https://doi.org/10.11121/ijocta.01.2011.0035

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Section

Fractional Dynamics and Control