An Inverse Coefficient Problem for a Parabolic Equation under Nonlocal Boundary and Integral Overdetermination Conditions

Oussaeif Taki-Eddine^1, and Bouziani Abdelfatah¹

¹Department of Mathematics and Informatics, the Larbi Ben M.hidi University, Oum El Bouaghi

Cite this paper:
Oussaeif Taki-Eddine and Bouziani Abdelfatah. An Inverse Coefficient Problem for a Parabolic Equation under Nonlocal Boundary and Integral Overdetermination Conditions. International Journal of Partial Differential Equations and Applications. 2014; 2(3):38-43. doi: 10.12691/ijpdea-2-3-1

Abstract

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.

Keywords:
heat equation inverse problem nonlocal boundary condition integral overdetermination condition Fourier method

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