Fourier series analysis of a time-dependent perfusion coefficient determination in a 2D bioheat transfer process

In this work, an inverse problem of determining the time-dependent perfusion coefficient of two-dimensional (2D) heat equation with a classical and total energy integral overdetermination condition is considered. The existence and uniqueness of the problem is obtained by generalized Fourier method combined with the unique solvability of the second kind Volterra integral equation. Moreover, the proof of the continuous dependence upon the data of the inverse problem is given.