Recovery of a time-dependent heat source in one-dimensional thermoelasticity of type-III.

In this contribution, the reconstruction of a solely time-dependent heat source is studied in an inverse problem arising in one-dimensional thermoelasticity. The missing heat source is recovered from a measurement in time of the average temperature inside the body. Using this observation, the inverse problem is reformulated in a direct setting. The existence and uniqueness of a weak solution are addressed, and a new numerical algorithm based on Rothe’s method is designed. Numerical experiments support the obtained results. [ABSTRACT FROM AUTHOR]