%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 Greenâ€™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