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