Problems of determining the temperature and density of heat sources from the initial and final temperatures

Determination of an unknown source term and the temperature distribution for the linear heat equation involving fractional derivative in time

“…These kind of problems are ill posed in the sense of Hadamard. A number of articles address the solvability problem of the inverse problems (see [1], [2], [3], [4], [5], [6], [7], [8] and references therein).…”

On an inverse problem of reconstructing a subdiffusion process from nonlocal data

“…In Ahmad et al, there are good references to publications on related issues. We note from recent papers close to the theme of our article. In these papers, different variants of direct and inverse initial‐boundary value problems for evolutionary equations are considered, including problems with nonlocal boundary conditions and problems for equations with fractional derivatives.…”

“…(A) Let (x), (x) ∈ W 2 2 (− , ) and satisfy the boundary conditions (10). Then for a real number such that | | < 1 the inverse problems (1) to (3) and (25) have a unique generalized solution, which is stable in norm:…”

“…In deriving these inequalities, we use the fact that the functions (x), (x) satisfy the boundary conditions (10). Now, we can easily obtain an estimate for t − D t Φ (x, t) from Equation 5.…”

Inverse problems for a nonlocal wave equation with an involution perturbation

“…Also, differential equations with operations on the space variable received great attention starting with Carleman [6] (equations with shift (involution)) and followed with great attention by Przewoerska-Rolewicz [17,18,19,20,21,22,23], Aftabizadeh et al [1], Andreev [3], [4], Burlutskayaa et al [5], Gupta [7], [8], [9], Watkins [31], Viner [29], [30], and Wiener [32], [33]; for spectral problems and inverse problems for equations with involutions we may cite the recent works of Kaliev et al [10], [11], Sadybekov et al [15], [16], [25], Sarsenbi et al [13], [26] and [27]. The papers of Aliev [2] and Rus [24] concern the maximum principle for equations with a delay in the space variable.…”