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

Yuriy Povstenko | Zendy

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

Author(s) -

Yuriy Povstenko

Publication year - 2011

Publication title -

an international journal of optimization and control theories and applications (ijocta)

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.287

H-Index - 6

eISSN - 2146-5703

pISSN - 2146-0957

DOI - 10.11121/ijocta.01.2011.0035

Subject(s) - spherical coordinate system , mathematical analysis , laplace transform , cylindrical coordinate system , fourier transform , diffusion equation , legendre polynomials , mathematics , dirichlet boundary condition , laplace's equation , coordinate system , spherical mean , spherical harmonics , legendre transformation , wave equation , boundary value problem , physics , geometry , economy , economics , service (business)

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 I•, 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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