Science and Education Publishing International Journal of Partial Differential Equations and Applications 2 3 2014 06 19 An Inverse Coefficient Problem for a Parabolic Equation under Nonlocal Boundary and Integral Overdetermination Conditions 38 43 EN Oussaeif Taki-Eddine Department of Mathematics and Informatics, the Larbi Ben M.hidi University, Oum El Bouaghi Bouziani Abdelfatah IJPDEA2014231 10.12691/ijpdea-2-3-1 2014 06 03 2014 06 16 2014 06 19 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.