eng Science and Education Publishing International Journal of Partial Differential Equations and Applications 2014-06-19 2 3 38 43 10.12691/ijpdea-2-3-1 IJPDEA2014231 article Oussaeif Taki-Eddine taki_maths@live.fr 1 Bouziani Abdelfatah 1 Department of Mathematics and Informatics, the Larbi Ben M.hidi University, Oum El Bouaghi This paper investigates the inverse problem of simultaneously determining the time-dependent thermal diffusivity and the temperature distribution in a parabolic equation in the case of nonlocal boundary conditions containing a real parameter and integral overdetermination conditions. Under some consistency conditions on the input data the existence, uniqueness and continuously dependence upon the data of the classical solution are shown by using the generalized Fourier method. http://pubs.sciepub.com/ijpdea/2/3/1/ijpdea-2-3-1.pdf heat equation inverse problem nonlocal boundary condition integral overdetermination condition Fourier method