Equations with Three Space Variables in Spherical Coordinates

Yuriy Povstenko
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Yuriy Povstenko: Jan Długosz University in Częstochowa

Chapter Chapter 12 in Linear Fractional Diffusion-Wave Equation for Scientists and Engineers, 2015, pp 415-431 from Springer

Abstract: Abstract Consider the time-fractional diffusion-wave equation with a source term in spherical coordinates r,θand φ: $$\frac{\partial^\alpha T}{\partial t^\alpha}\;=\;a\Bigg[\frac{\partial^2 T}{\partial r^2}\;+\frac{2}{r}\;\frac{\partial T}{\partial r}\;+\frac{1}{r^2 \mathrm{sin}\;\theta}\;\frac{\partial}{\partial\theta}\Bigg(\mathrm{sin}\;\theta\frac{\partial T}{\partial\theta}\Bigg)\;+\;\frac{1}{r^2\mathrm{sin}^2\theta}\frac{\partial^2 T}{\partial \varphi^2}\Bigg]+\;\Phi(r,\theta,\varphi,t),\qquad \qquad 0\leq r\leq\infty, 0\leq \theta\leq \pi, 0\leq\varphi\leq 2\pi.$$

Date: 2015
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DOI: 10.1007/978-3-319-17954-4_12

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