Uniqueness for inverse source problems of determining a space-dependent source in thermoelastic systems

Y We study the uniqueness of some inverse source problems arising in thermoelastic models of typeIII. We suppose that the source terms can be decomposed as a product of a time dependent and a space dependent function, i.e. g(t)f(x) for the load source and g(t)f(x) for the heat source. In the first inverse source problem, the source f(x) has to be determined fromthe final in time measurement of the displacement u(x, T), or fromthe time-average measurement integral (T)(0) u(x, t) dt. In the second inverse source problem, the source f(x) has to be determined from the time-average measurement of the temperature integral(T)(0) theta(x, t) dt. We show the uniqueness of a solution to these problems under suitable assumptions on the function g(t). Moreover, we provide some examples showing the necessity of these assumptions. Finally, we conclude the article by studying two combined problems of determining both sources.