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

Yuriy POVSTENKO
2011 An International Journal of Optimization and Control: Theories & Applications  
Non-axisymmetric 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 ϕ, 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
more » ... ntral symmetric case with one spatial coordinate r the obtained results coincide with those studied earlier. 3 and the prescribed boundary value of the sought-for function r = R : G g = g 0 δ(µ − ζ) δ(ϕ − φ) δ + (t). (59) α = 0.5 © α = 1 © α = 1.5 © α = 1.65 © Dependence of fundamental solution (61) on the coordinates r, µ, and ϕ is presented in Figures 4-6 withḠ g = tG g /g 0 . α = 0.5 © α = 1 © α = 1.5 © α = 0.5 © α = 1 © α = 1.5 ©
doi:10.11121/ijocta.01.2011.0035 fatcat:oxyfwiop2zex7fxcgbhxogqrp4