The paper deals with the reconstruction of the convolution kernel, together with the solution, in a mixed linear evolution system of hyperbolic type. This problem describes uniaxial deformations u of a cylindrical domain (0,π) × Ω, which is filled with a linear viscoelastic solid whose material properties are supposed to be uniform on Ω-sections perpendicular to the x axis. Various types of boundary conditions in [0,T] × 0,π × Ω are prescribed, whereas Dirichlet conditions are assumed in [0,T] × (0,π) × ∂Ω. To reconstruct both u and k, we suppose of knowing for any time tand any x ∈ (0,π) the flux of the viscoelastic stress vector through the boundary of the Ω-section. The main novelty is that the unknown kernel k is allowed to depend, not only on the time variable t but also on the space variable x.

Giorgi, C., Guidetti, D. (2018). Reconstruction of kernel depending also on space variable. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 41(12), 4560-4588 [10.1002/mma.4914].

Reconstruction of kernel depending also on space variable

Guidetti, Davide
2018

Abstract

The paper deals with the reconstruction of the convolution kernel, together with the solution, in a mixed linear evolution system of hyperbolic type. This problem describes uniaxial deformations u of a cylindrical domain (0,π) × Ω, which is filled with a linear viscoelastic solid whose material properties are supposed to be uniform on Ω-sections perpendicular to the x axis. Various types of boundary conditions in [0,T] × 0,π × Ω are prescribed, whereas Dirichlet conditions are assumed in [0,T] × (0,π) × ∂Ω. To reconstruct both u and k, we suppose of knowing for any time tand any x ∈ (0,π) the flux of the viscoelastic stress vector through the boundary of the Ω-section. The main novelty is that the unknown kernel k is allowed to depend, not only on the time variable t but also on the space variable x.
2018
Giorgi, C., Guidetti, D. (2018). Reconstruction of kernel depending also on space variable. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 41(12), 4560-4588 [10.1002/mma.4914].
Giorgi, Claudio*; Guidetti, Davide
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/677901
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