Data di Pubblicazione:
2019
Citazione:
The structure of the fractional powers of the noncommutative Fourier law / F. Colombo, M.M. Peloso, S. Pinton. - In: MATHEMATICAL METHODS IN THE APPLIED SCIENCES. - ISSN 0170-4214. - (2019 Jun 17). [Epub ahead of print] [10.1002/mma.5719]
Abstract:
In the recent years, there has been a lot of interest in fractional diffusion and fractional evolution problems. The spectral theory on the S-spectrum turned out to be an important tool to define new fractional diffusion operators stating from the Fourier law for nonhomogeneous materials. Precisely, let eℓ, eℓ=1,2,3 be orthogonal unit vectors in R3 and let Ω ⊂ R3 be a bounded open set with smooth boundary ∂Ω. Denoting by (Formula presented.) a point in Ω, the heat equation is obtained replacing the Fourier law given by (Formula presented.) into the conservation of energy law. In this paper, we investigate the structure of the fractional powers of the vector operator T, with homogeneous Dirichlet boundary conditions. Recently, we have found sufficient conditions on the coefficients a, b, c : Ω → R such that the fractional powers of T exist in the sense of the S-spectrum approach. In this paper, we show that under a different set of conditions on the coefficients a, b, c, the fractional powers of T have a different structure.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
fractional diffusion processes; fractional powers of vector operators; S-spectrum; structure of the fractional fourier's law; the S-spectrum approach
Elenco autori:
F. Colombo, M.M. Peloso, S. Pinton
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