Inverse problems for identification of memory kernels in thermo- and poro-viscoelasticity

A stability result via Carleman estimates for an inverse source problem related to a hyperbolic integro-differential equation

“…In a forthcoming paper, we discuss the details. Different kinds of inverse problems, which consist in determining time-dependent factors in the kernel K (x, t, η), are dealt with, e.g., in the papers by Cavaterra [4], Cavaterra and Grasselli [5], Cavaterra and Lorenzi [6], Janno and Lorenzi [15], Janno and von Wolfersdorf [16], Kabanikhin and Lorenzi [17], Lorenzi [24], Lorenzi and Messina [25], [26], Lorenzi and Romanov [27], Lorenzi and Yahkno [28], von Wolfersdorf [29] and the references therein.…”

A stability result via Carleman estimates for an inverse source problem related to a hyperbolic integro-differential equation

“…In a forthcoming paper, we discuss the details. Different kinds of inverse problems, which consist in determining time-dependent factors in the kernel K (x, t, η), are dealt with, e.g., in the papers by Cavaterra [4], Cavaterra and Grasselli [5], Cavaterra and Lorenzi [6], Janno and Lorenzi [15], Janno and von Wolfersdorf [16], Kabanikhin and Lorenzi [17], Lorenzi [24], Lorenzi and Messina [25], [26], Lorenzi and Romanov [27], Lorenzi and Yahkno [28], von Wolfersdorf [29] and the references therein.…”

Inverse Problems for Memory Kernels by Laplace Transform Methods

“…An analogous parabolic integro-differential equation as (1) occurs in the theory of flow in porous media where u now denotes the pressure, λ = κρ with permeability κ and mass density ρ again, β is the reciprocal of Biot's modulus with the corresponding memory kernel m and f is the mass source density (cf. [15], for instance). Besides equation (1) the function u satisfies the initial and boundary conditions…”

“…follow. Equations (10) and 11for the additional conditions (4) and (5) in the inverse problems are transformed to the equations (15) and (16) again.…”