Retrieving the time-dependent thermal conductivity of an orthotropic rectangular conductor

Inverse problems for a perturbed time fractional diffusion equation with final overdetermination

“…This equation enables an immediate integration. Applying the operator of fractional integration I 1− = t − Γ(1− ) * of the order 1 − to (5), we obtain the equation u = (Δu + m * Δu) + F…”

“…The aim is to find a function f such that the solution u of (8) with F of the form (10) satisfies the condition (9). We mention that in terms of the physical source function Q occurring in (5), the formula (10) has the form…”

“…Sometimes parameters of processes or models (coefficients of equations, source terms, initial or boundary conditions) are unknown. To determine unknown parameters, inverse problems that involve observation of states of processes are solved …”

“…To determine unknown parameters, inverse problems that involve observation of states of processes are solved. [5][6][7][8][9][10] Usually an observation of a state over a whole space-time domain is not possible or not practical. Depending on possibilities or unknowns to be recovered, measurements of the state in a subdomain, at a boundary of a space domain or at a final time moment, are used in the reconstruction.…”

Reconstruction of an orthotropic thermal conductivity from non-local heat flux measurements

“…However, in the time-dependent case the scenario has received limited attention from researchers. Here, we only highlight the nonlinear identification of a temperature-dependent orthotropic material, [18], the recovery of the leading coefficients of a heterogeneous orthotropic medium, [8,9,14], and the space-dependent anisotropic case addressed in [12].…”