On the determination of additive source terms in the hyperbolic bio-heat equation

We study the simultaneous recovery of two additive source components in the two-dimensional hyperbolic bio-heat equation from temperature measurements at two spatial cross-sections. The inverse problem is reduced to a source-free initial–boundary value problem for the mixed spatial derivative of the temperature. Using energy estimates, we prove the unique solvability of the inverse source problem and establish convergence to the parabolic limit at a rate proportional to the square root of the time-lag relaxation parameter.