A parabolic inverse source problem with a dynamical boundary condition

An inverse time-dependent source problem for the heat equation with a non-classical boundary condition

“…where σ is a given Lipschitz function, has very recently been investigated in [26]. However, no numerical results were presented and the boundary condition (1.7) is different of the boundary condition (1.5) considered in the present study.…”

On the Inverse Problems for a Family of Integro-Differential Equations

“…The direct and inverse problems with dynamic boundary conditions for heat equation have been considered by many authors, for readers convenience, we refer [4,7,9,10,11,20,23]. In last few years, the diffusion equations involving integrals and derivatives of fractional order are considered extensively in literature.…”

Identification of source terms in heat equation with dynamic boundary conditions

“…The gradient formula (25) for the Tikhonov functional J 𝜀 allows us to implement classical versions of the Conjugate Gradient Algorithm with different conjugation coefficients. Here, we shall restrict ourselves to the following basic algorithm.…”

“…In the present work, we extend the previous technique for the determination of two source terms acting in both, in the domain and on the boundary, in heat equation with dynamic boundary conditions. In this context, we mention Slodika 25 for the identification of a time-dependent source term from the knowledge of a space average using the backward Euler method. Also, in Ismailov, 26 the author deals with a time-dependent source from an integral overdetermination condition in a 1-D heat equation by using the generalized Fourier method.…”