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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.