%0 Journal Article %T The time-dependent diffusion equation: An inverse diffusivity problem %J Iranian Journal of Numerical Analysis and Optimization %I Ferdowsi University of Mashhad %Z 2423-6977 %A Tabasi, S.H. %A Mazraeh, H.D. %A Irani, A.A. %A Pourgholi, R. %A Esfahani, A. %D 2021 %\ 03/01/2021 %V 11 %N 1 %P 33-54 %! The time-dependent diffusion equation: An inverse diffusivity problem %K Inverse parabolic problem %K existence %K Uniqueness %K Green’s function %K Fixed point %K Contraction mapping %K Genetic algorithm %R 10.22067/ijnao.2021.11309.0 %X We find a solution of an unknown time-dependent diffusivity a(t) in a linear inverse parabolic problem by a modified genetic algorithm. At first, it is shown that under certain conditions of data, there exists at least one solution for unknown a(t) in (a(t), T (x, t)), which is a solution to the corresponding problem. Then, an optimal estimation for unknown a(t) is found by applying the least-squares method and a modified genetic algo rithm. Results show that an excellent estimation can be obtained by the implementation of a modified real-valued genetic algorithm within an Intel Pentium (R) dual-core CPU with a clock speed of 2.4 GHz. %U https://ijnao.um.ac.ir/article_39498_4e70303762f92c47958ef68e7d4ce560.pdf